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class="vector-toc-list"> <li id="toc-Life_insurance,_pensions_and_healthcare" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Life_insurance,_pensions_and_healthcare"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Life insurance, pensions and healthcare</span> </div> </a> <ul id="toc-Life_insurance,_pensions_and_healthcare-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_to_other_forms_of_insurance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Applications_to_other_forms_of_insurance"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Applications to other forms of insurance</span> </div> </a> <ul id="toc-Applications_to_other_forms_of_insurance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Actuaries_in_criminal_justice" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Actuaries_in_criminal_justice"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Actuaries in criminal justice</span> </div> </a> <ul id="toc-Actuaries_in_criminal_justice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Actuarial_science_related_to_modern_financial_economics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Actuarial_science_related_to_modern_financial_economics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Actuarial science related to modern financial economics</span> </div> </a> <ul id="toc-Actuarial_science_related_to_modern_financial_economics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Pre-formalisation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pre-formalisation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Pre-formalisation</span> </div> </a> <ul id="toc-Pre-formalisation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Initial_development" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Initial_development"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Initial development</span> </div> </a> <ul id="toc-Initial_development-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Early_actuaries" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_actuaries"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Early actuaries</span> </div> </a> <ul id="toc-Early_actuaries-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Technological_advances" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Technological_advances"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Technological advances</span> </div> </a> <ul id="toc-Technological_advances-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Works_cited" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Works_cited"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Works cited</span> </div> </a> <ul id="toc-Works_cited-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Actuarial science</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 32 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-32" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">32 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Aktuari%C3%ABle_wetenskap" title="Aktuariële wetenskap – Afrikaans" lang="af" hreflang="af" data-title="Aktuariële wetenskap" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%84%D9%85_%D8%A3%D9%83%D8%AA%D9%88%D8%A7%D8%B1%D9%8A" title="علم أكتواري – Arabic" lang="ar" hreflang="ar" data-title="علم أكتواري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Aktuar_hesablamalar" title="Aktuar hesablamalar – Azerbaijani" lang="az" hreflang="az" data-title="Aktuar hesablamalar" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%AE%E0%A6%BE%E0%A6%97%E0%A6%A3%E0%A6%A8%E0%A6%BE_%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="বীমাগণনা বিজ্ঞান – Bangla" lang="bn" hreflang="bn" data-title="বীমাগণনা বিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D1%83%D0%B0%D1%80%D0%BD%D1%8B%D1%8F_%D1%80%D0%B0%D0%B7%D0%BB%D1%96%D0%BA%D1%96" title="Актуарныя разлікі – Belarusian" lang="be" hreflang="be" data-title="Актуарныя разлікі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Pojistn%C3%A1_matematika" title="Pojistná matematika – Czech" lang="cs" hreflang="cs" data-title="Pojistná matematika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Gwyddor_actiwaraidd" title="Gwyddor actiwaraidd – Welsh" lang="cy" hreflang="cy" data-title="Gwyddor actiwaraidd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Forsikringsvidenskab" title="Forsikringsvidenskab – Danish" lang="da" hreflang="da" data-title="Forsikringsvidenskab" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Versicherungsmathematik" title="Versicherungsmathematik – German" lang="de" hreflang="de" data-title="Versicherungsmathematik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kindlustusmatemaatika" title="Kindlustusmatemaatika – Estonian" lang="et" hreflang="et" data-title="Kindlustusmatemaatika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BD%CE%B1%CE%BB%CE%BF%CE%B3%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE_%CE%B5%CF%80%CE%B9%CF%83%CF%84%CE%AE%CE%BC%CE%B7" title="Αναλογιστική επιστήμη – Greek" lang="el" hreflang="el" data-title="Αναλογιστική επιστήμη" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es badge-Q70893996 mw-list-item" title=""><a href="https://es.wikipedia.org/wiki/Ciencia_actuarial" title="Ciencia actuarial – Spanish" lang="es" hreflang="es" data-title="Ciencia actuarial" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Asekura_matematiko" title="Asekura matematiko – Esperanto" lang="eo" hreflang="eo" data-title="Asekura matematiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%DB%8C%D9%85%E2%80%8C%D8%B3%D9%86%D8%AC%DB%8C" title="بیم‌سنجی – Persian" lang="fa" hreflang="fa" data-title="بیم‌سنجی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Science_actuarielle" title="Science actuarielle – French" lang="fr" hreflang="fr" data-title="Science actuarielle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%B4%ED%97%98%EA%B3%84%EB%A6%AC%ED%95%99" title="보험계리학 – Korean" lang="ko" hreflang="ko" data-title="보험계리학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%AE%E0%A4%BE_%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8" title="बीमा विज्ञान – Hindi" lang="hi" hreflang="hi" data-title="बीमा विज्ञान" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ilmu_aktuaria" title="Ilmu aktuaria – Indonesian" lang="id" hreflang="id" data-title="Ilmu aktuaria" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A7%D7%98%D7%95%D7%90%D7%A8%D7%99%D7%94" title="אקטואריה – Hebrew" lang="he" hreflang="he" data-title="אקטואריה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sains_aktuari" title="Sains aktuari – Malay" lang="ms" hreflang="ms" data-title="Sains aktuari" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BF%9D%E9%99%BA%E6%95%B0%E7%90%86" title="保険数理 – Japanese" lang="ja" hreflang="ja" data-title="保険数理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%90%E0%A8%95%E0%A8%9A%E0%A9%81%E0%A8%B0%E0%A9%80%E0%A8%85%E0%A8%B2_%E0%A8%B8%E0%A8%BE%E0%A8%87%E0%A9%B0%E0%A8%B8" title="ਐਕਚੁਰੀਅਲ ਸਾਇੰਸ – Punjabi" lang="pa" hreflang="pa" data-title="ਐਕਚੁਰੀਅਲ ਸਾਇੰਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Matematyka_ubezpieczeniowa" title="Matematyka ubezpieczeniowa – Polish" lang="pl" hreflang="pl" data-title="Matematyka ubezpieczeniowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ci%C3%AAncias_atuariais" title="Ciências atuariais – Portuguese" lang="pt" hreflang="pt" data-title="Ciências atuariais" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D1%83%D0%B0%D1%80%D0%BD%D1%8B%D0%B5_%D1%80%D0%B0%D1%81%D1%87%D1%91%D1%82%D1%8B" title="Актуарные расчёты – Russian" lang="ru" hreflang="ru" data-title="Актуарные расчёты" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Agham_pang-aktuwaryo" title="Agham pang-aktuwaryo – Tagalog" lang="tl" hreflang="tl" data-title="Agham pang-aktuwaryo" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AE%BF%E0%AE%A4%E0%AE%BF_%E0%AE%87%E0%AE%9F%E0%AE%B0%E0%AF%8D%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="நிதி இடர்க் கணிப்பியல் – Tamil" lang="ta" hreflang="ta" data-title="நிதி இடர்க் கணிப்பியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%81%E0%B8%B1%E0%B8%99%E0%B8%A0%E0%B8%B1%E0%B8%A2" title="คณิตศาสตร์ประกันภัย – Thai" lang="th" hreflang="th" data-title="คณิตศาสตร์ประกันภัย" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D1%83%D0%B0%D1%80%D0%BD%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Актуарна математика – Ukrainian" lang="uk" hreflang="uk" data-title="Актуарна математика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%AD%D8%B5%D8%A7%D8%A6%DB%8C_%D8%B9%D9%84%D9%88%D9%85" title="احصائی علوم – Urdu" lang="ur" hreflang="ur" data-title="احصائی علوم" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B2%BE%E7%AE%97%E5%AD%B8" title="精算學 – Cantonese" lang="yue" hreflang="yue" data-title="精算學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%B2%BE%E7%AE%97%E5%AD%B8" title="精算學 – Chinese" lang="zh" hreflang="zh" data-title="精算學" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1128453#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div 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class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Actuarial_mathematics&redirect=no" class="mw-redirect" title="Actuarial mathematics">Actuarial mathematics</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Statistics applied to risk in insurance and other financial products</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Excerpt_from_CDC_2003_Table_1.pdf" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Excerpt_from_CDC_2003_Table_1.pdf/page1-220px-Excerpt_from_CDC_2003_Table_1.pdf.jpg" decoding="async" width="220" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Excerpt_from_CDC_2003_Table_1.pdf/page1-330px-Excerpt_from_CDC_2003_Table_1.pdf.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Excerpt_from_CDC_2003_Table_1.pdf/page1-440px-Excerpt_from_CDC_2003_Table_1.pdf.jpg 2x" data-file-width="1275" data-file-height="1650" /></a><figcaption>2003 US mortality (<a href="/wiki/Life_table" title="Life table">life</a>) table, Table 1, Page 1</figcaption></figure> <p><b>Actuarial science</b> is the discipline that applies <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> and <a href="/wiki/Statistics" title="Statistics">statistical</a> methods to <a href="/wiki/Risk_assessment" title="Risk assessment">assess risk</a> in <a href="/wiki/Insurance" title="Insurance">insurance</a>, <a href="/wiki/Pension" title="Pension">pension</a>, <a href="/wiki/Finance" title="Finance">finance</a>, <a href="/wiki/Investment" title="Investment">investment</a> and other industries and professions. </p><p><a href="/wiki/Actuary" title="Actuary">Actuaries</a> are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis. </p><p>Actuarial science includes a number of interrelated subjects, including mathematics, <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a>, statistics, finance, <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Financial_accounting" title="Financial accounting">financial accounting</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a>. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> actuarial models with modern financial theory.<sup id="cite_ref-FOOTNOTEFrees1990_1-0" class="reference"><a href="#cite_note-FOOTNOTEFrees1990-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Many universities have undergraduate and graduate degree programs in actuarial science. In 2010,<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The date of the event predicted near this tag has passed. (July 2021)">needs update</span></a></i>]</sup> a study published by job search website CareerCast ranked actuary as the #1 job in the United States.<sup id="cite_ref-FOOTNOTENeedleman2010_2-0" class="reference"><a href="#cite_note-FOOTNOTENeedleman2010-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands, and stress. In 2024, <i><a href="/wiki/U.S._News_%26_World_Report" title="U.S. News & World Report">U.S. News & World Report</a></i> ranked actuary as the third-best job in the business sector and the eighth-best job in <a href="/wiki/STEM" class="mw-redirect" title="STEM">STEM</a>.<sup id="cite_ref-FOOTNOTEU.S._News_&_World_Report2024_3-0" class="reference"><a href="#cite_note-FOOTNOTEU.S._News_&_World_Report2024-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Subfields">Subfields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=1" title="Edit section: Subfields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Life_insurance,_pensions_and_healthcare"><span id="Life_insurance.2C_pensions_and_healthcare"></span>Life insurance, pensions and healthcare</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=2" title="Edit section: Life insurance, pensions and healthcare"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage such as burial, <a href="/wiki/Life_insurance" title="Life insurance">life insurance</a>, and annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future. This requires estimating future contingent events, such as the rates of mortality by age, as well as the development of mathematical techniques for discounting the value of funds set aside and invested. This led to the development of an important actuarial concept, referred to as the <a href="/wiki/Present_value" title="Present value">present value</a> of a future sum. Certain aspects of the actuarial methods for discounting <a href="/wiki/Pension_funds" class="mw-redirect" title="Pension funds">pension funds</a> have come under criticism from modern <a href="/wiki/Financial_economics" title="Financial economics">financial economics</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p> <ul><li>In traditional life insurance, actuarial science focuses on the analysis of <a href="/wiki/Mortality_rate" title="Mortality rate">mortality</a>, the production of <a href="/wiki/Life_table" title="Life table">life tables</a>, and the application of <a href="/wiki/Interest" title="Interest">compound interest</a> to produce life insurance, annuities and endowment policies. Contemporary life insurance programs have been extended to include credit and mortgage insurance, <a href="/wiki/Key_person_insurance" title="Key person insurance">key person insurance</a> for small businesses, <a href="/wiki/Long_term_care_insurance" class="mw-redirect" title="Long term care insurance">long term care insurance</a> and <a href="/wiki/Medical_savings_account" title="Medical savings account">health savings accounts</a>.<sup id="cite_ref-FOOTNOTEHsiao2001_4-0" class="reference"><a href="#cite_note-FOOTNOTEHsiao2001-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>In health insurance, including insurance provided directly by employers, and social insurance, actuarial science focuses on the analysis of rates of disability, morbidity, mortality, fertility and other contingencies. The effects of <a href="/wiki/Consumer_choice" title="Consumer choice">consumer choice</a> and the geographical distribution of the utilization of medical services and procedures, and the utilization of drugs and therapies, is also of great importance. These factors underlay the development of the <a href="/wiki/Resource-based_relative_value_scale" title="Resource-based relative value scale">Resource-Base Relative Value Scale</a> (RBRVS) at Harvard in a multi-disciplined study.<sup id="cite_ref-FOOTNOTEHsiao2004_5-0" class="reference"><a href="#cite_note-FOOTNOTEHsiao2004-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government standards on the cost of healthcare.<sup id="cite_ref-FOOTNOTECHBRP2004_6-0" class="reference"><a href="#cite_note-FOOTNOTECHBRP2004-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li>In the pension industry, actuarial methods are used to measure the costs of alternative strategies with regard to the design, funding, accounting, administration, and maintenance or redesign of pension plans. The strategies are greatly influenced by short-term and long-term bond rates, the funded status of the pension and benefit arrangements, <a href="/wiki/Collective_bargaining" title="Collective bargaining">collective bargaining</a>; the employer's old, new and foreign competitors; the changing demographics of the workforce; changes in the internal revenue code; changes in the attitude of the internal revenue service regarding the calculation of surpluses; and equally importantly, both the short and long term financial and economic trends. It is common with mergers and acquisitions that several pension plans have to be combined or at least administered on an equitable basis. When benefit changes occur, old and new benefit plans have to be blended, satisfying new social demands and various government discrimination test calculations, and providing employees and retirees with understandable choices and transition paths. Benefit plans liabilities have to be properly valued, reflecting both earned benefits for past service, and the benefits for future service. Finally, funding schemes have to be developed that are manageable and satisfy the standards board or regulators of the appropriate country, such as the <a href="/wiki/Financial_Accounting_Standards_Board" title="Financial Accounting Standards Board">Financial Accounting Standards Board</a> in the United States.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup></li> <li>In social welfare programs, the <a href="/wiki/Office_of_the_Chief_Actuary" title="Office of the Chief Actuary">Office of the Chief Actuary</a> (OCACT), <a href="/wiki/Social_Security_Administration" title="Social Security Administration">Social Security Administration</a> plans and directs a program of actuarial estimates and analyses relating to SSA-administered retirement, survivors and disability insurance programs and to proposed changes in those programs. It evaluates operations of the <a href="/wiki/Social_Security_(United_States)" title="Social Security (United States)">Federal Old-Age and Survivors Insurance Trust Fund</a> and the Federal Disability Insurance Trust Fund, conducts studies of program financing, performs actuarial and demographic research on social insurance and related program issues involving mortality, morbidity, utilization, retirement, disability, survivorship, marriage, unemployment, poverty, old age, families with children, etc., and projects future workloads. In addition, the Office is charged with conducting cost analyses relating to the <a href="/wiki/Supplemental_Security_Income" title="Supplemental Security Income">Supplemental Security Income</a> (SSI) program, a general-revenue financed, means-tested program for low-income aged, blind and disabled people. The office provides technical and consultative services to the Commissioner, to the board of trustees of the Social Security Trust Funds, and its staff appears before Congressional Committees to provide expert testimony on the actuarial aspects of Social Security issues.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Applications_to_other_forms_of_insurance">Applications to other forms of insurance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=3" title="Edit section: Applications to other forms of insurance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Actuarial science is also applied to <a href="/wiki/Property_insurance" title="Property insurance">property</a>, <a href="/wiki/Casualty_insurance" title="Casualty insurance">casualty</a>, <a href="/wiki/Liability_insurance" title="Liability insurance">liability</a>, and <a href="/wiki/General_insurance" title="General insurance">general insurance</a>. In these forms of insurance, coverage is generally provided on a renewable period, (such as a yearly). Coverage can be cancelled at the end of the period by either party.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p><p><a href="/wiki/Property_insurance" title="Property insurance">Property</a> and <a href="/wiki/Casualty_insurance" title="Casualty insurance">casualty insurance</a> companies tend to specialize because of the complexity and diversity of risks.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2010)">citation needed</span></a></i>]</sup> One division is to organize around personal and commercial lines of insurance. Personal lines of insurance are for individuals and include fire, auto, homeowners, theft and umbrella coverages. Commercial lines address the insurance needs of businesses and include property, business continuation, product liability, fleet/commercial vehicle, workers compensation, fidelity and surety, and <a href="/wiki/Directors_and_officers_liability_insurance" title="Directors and officers liability insurance">D&O</a> insurance. The insurance industry also provides coverage for exposures such as catastrophe, weather-related risks, earthquakes, patent infringement and other forms of corporate espionage, terrorism, and "one-of-a-kind" (e.g., satellite launch). Actuarial science provides data collection, measurement, estimating, forecasting, and valuation tools to provide financial and underwriting data for management to assess marketing opportunities and the nature of the risks. Actuarial science often helps to assess the overall risk from catastrophic events in relation to its underwriting capacity or surplus.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p><p>In the <a href="/wiki/Reinsurance" title="Reinsurance">reinsurance</a> fields, actuarial science can be used to design and price reinsurance and retrocession arrangements, and to establish reserve funds for known claims and future claims and catastrophes.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Actuaries_in_criminal_justice">Actuaries in criminal justice</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=4" title="Edit section: Actuaries in criminal justice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is an increasing trend to recognize that actuarial skills can be applied to a range of applications outside the traditional fields of insurance, pensions, etc. One notable example is the use in some US states of actuarial models to set criminal sentencing guidelines. These models attempt to predict the chance of re-offending according to rating factors which include the type of crime, age, educational background and ethnicity of the offender.<sup id="cite_ref-FOOTNOTESilverChow-Martin2002_7-0" class="reference"><a href="#cite_note-FOOTNOTESilverChow-Martin2002-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> However, these models have been open to criticism as providing justification for discrimination against specific ethnic groups by law enforcement personnel. Whether this is statistically correct or a self-fulfilling correlation remains under debate.<sup id="cite_ref-FOOTNOTEHarcourt2003_8-0" class="reference"><a href="#cite_note-FOOTNOTEHarcourt2003-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Another example is the use of actuarial models to assess the risk of sex offense recidivism. Actuarial models and associated tables, such as the MnSOST-R, Static-99, and SORAG, have been used since the late 1990s to determine the likelihood that a sex offender will re-offend and thus whether he or she should be institutionalized or set free.<sup id="cite_ref-FOOTNOTENietoJung200628–33_9-0" class="reference"><a href="#cite_note-FOOTNOTENietoJung200628–33-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Actuarial_science_related_to_modern_financial_economics">Actuarial science related to modern financial economics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=5" title="Edit section: Actuarial science related to modern financial economics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Traditional actuarial science and modern <a href="/wiki/Financial_economics" title="Financial economics">financial economics</a> in the US have different practices, which is caused by different ways of calculating funding and investment strategies, and by different regulations.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p><p>Regulations are from the <a href="/w/index.php?title=Armstrong_investigation_of_1905&action=edit&redlink=1" class="new" title="Armstrong investigation of 1905 (page does not exist)">Armstrong investigation of 1905</a>, the <a href="/wiki/Glass%E2%80%93Steagall_Act_of_1932" title="Glass–Steagall Act of 1932">Glass–Steagall Act of 1932</a>, the adoption of the <a href="/w/index.php?title=Mandatory_Security_Valuation_Reserve&action=edit&redlink=1" class="new" title="Mandatory Security Valuation Reserve (page does not exist)">Mandatory Security Valuation Reserve</a> by the <a href="/wiki/National_Association_of_Insurance_Commissioners" title="National Association of Insurance Commissioners">National Association of Insurance Commissioners</a>, which cushioned market fluctuations, and the <a href="/wiki/Financial_Accounting_Standards_Board" title="Financial Accounting Standards Board">Financial Accounting Standards Board</a>, (FASB) in the US and Canada, which regulates pensions valuations and funding.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=6" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Actuary#History" title="Actuary">Actuary § History</a></div> <p>Historically, much of the foundation of actuarial theory predated modern financial theory. In the early twentieth century, actuaries were developing many techniques that can be found in modern financial theory, but for various historical reasons, these developments did not achieve much recognition.<sup id="cite_ref-FOOTNOTEWhelan2002_10-0" class="reference"><a href="#cite_note-FOOTNOTEWhelan2002-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>As a result, actuarial science developed along a different path, becoming more reliant on assumptions, as opposed to the <a href="/wiki/Arbitrage-free" class="mw-redirect" title="Arbitrage-free">arbitrage-free</a> <a href="/wiki/Rational_pricing#Risk_neutral_valuation" title="Rational pricing">risk-neutral valuation</a> concepts used in modern finance. The divergence is not related to the use of historical data and statistical projections of liability cash flows, but is instead caused by the manner in which traditional actuarial methods apply market data with those numbers. For example, one traditional actuarial method suggests that changing the <a href="/wiki/Asset_allocation" title="Asset allocation">asset allocation</a> mix of investments can change the value of liabilities and assets (by changing the <a href="/wiki/Discounted_cash_flow" title="Discounted cash flow">discount rate</a> assumption). This concept is inconsistent with <a href="/wiki/Financial_economics" title="Financial economics">financial economics</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p><p>The potential of modern financial economics theory to complement existing actuarial science was recognized by actuaries in the mid-twentieth century.<sup id="cite_ref-FOOTNOTEBühlmann1997169–171_11-0" class="reference"><a href="#cite_note-FOOTNOTEBühlmann1997169–171-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In the late 1980s and early 1990s, there was a distinct effort for actuaries to combine financial theory and stochastic methods into their established models.<sup id="cite_ref-FOOTNOTED'Arcy1989_12-0" class="reference"><a href="#cite_note-FOOTNOTED'Arcy1989-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance.<sup id="cite_ref-FOOTNOTEEconomist2006_13-0" class="reference"><a href="#cite_note-FOOTNOTEEconomist2006-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Today, the profession, both in practice and in the educational syllabi of many actuarial organizations, is cognizant of the need to reflect the combined approach of tables, loss models, stochastic methods, and financial theory.<sup id="cite_ref-FOOTNOTEFeldblum20018–9_14-0" class="reference"><a href="#cite_note-FOOTNOTEFeldblum20018–9-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> However, assumption-dependent concepts are still widely used (such as the setting of the discount rate assumption as mentioned earlier), particularly in North America.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p><p>Product design adds another dimension to the debate. Financial economists argue that pension benefits are bond-like and should not be funded with equity investments without reflecting the risks of not achieving expected returns. But some pension products do reflect the risks of unexpected returns. In some cases, the pension beneficiary assumes the risk, or the employer assumes the risk. The current debate now seems to be focusing on four principles: </p> <ol><li>financial models should be free of arbitrage.</li> <li>assets and liabilities with identical cash flows should have the same price. This is at odds with <a href="/wiki/FASB" class="mw-redirect" title="FASB">FASB</a>.</li> <li>the value of an asset is independent of its financing.</li> <li>how pension assets should be invested</li></ol> <p>Essentially, financial economics state that pension assets should not be invested in equities for a variety of theoretical and practical reasons.<sup id="cite_ref-FOOTNOTEMoriarty2006_15-0" class="reference"><a href="#cite_note-FOOTNOTEMoriarty2006-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pre-formalisation">Pre-formalisation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=7" title="Edit section: Pre-formalisation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Elementary <a href="/wiki/Mutual_aid_(organization)" class="mw-redirect" title="Mutual aid (organization)">mutual aid</a> agreements and pensions arose in antiquity.<sup id="cite_ref-FOOTNOTEThucydides_16-0" class="reference"><a href="#cite_note-FOOTNOTEThucydides-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Early in the <a href="/wiki/Roman_Empire" title="Roman Empire">Roman empire</a>, associations were formed to meet the expenses of burial, cremation, and monuments—precursors to <a href="/wiki/Burial_society" title="Burial society">burial insurance</a> and <a href="/wiki/Friendly_society" title="Friendly society">friendly societies</a>. A small sum was paid into a communal fund on a weekly basis, and upon the death of a member, the fund would cover the expenses of rites and burial. These societies sometimes sold shares in the building of <a href="/wiki/Columbarium" title="Columbarium">columbāria</a>, or burial vaults, owned by the fund—the precursor to <a href="/wiki/Mutual_insurance" title="Mutual insurance">mutual insurance companies</a>.<sup id="cite_ref-FOOTNOTEJohnston1932§475–§476_17-0" class="reference"><a href="#cite_note-FOOTNOTEJohnston1932§475–§476-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Other early examples of mutual <a href="/wiki/Surety" title="Surety">surety</a> and assurance pacts can be traced back to various forms of fellowship within the Saxon clans of England and their Germanic forebears, and to Celtic society.<sup id="cite_ref-FOOTNOTELoan1992_18-0" class="reference"><a href="#cite_note-FOOTNOTELoan1992-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge.<sup id="cite_ref-FOOTNOTEFaculty_and_Institute_of_Actuaries2004_19-0" class="reference"><a href="#cite_note-FOOTNOTEFaculty_and_Institute_of_Actuaries2004-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Initial_development">Initial development</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=8" title="Edit section: Initial development"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The 17th century was a period of advances in mathematics in Germany, France and England. At the same time there was a rapidly growing desire and need to place the valuation of personal risk on a more scientific basis. Independently of each other, <a href="/wiki/Compound_interest" title="Compound interest">compound interest</a> was studied and <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a> emerged as a well-understood mathematical discipline. Another important advance came in 1662 from a London <a href="/wiki/Draper" title="Draper">draper</a>, the father of <a href="/wiki/Demography" title="Demography">demography</a>, <a href="/wiki/John_Graunt" title="John Graunt">John Graunt</a>, who showed that there were predictable patterns of longevity and death in a group, or <a href="/wiki/Cohort_(statistics)" title="Cohort (statistics)">cohort</a>, of people of the same age, despite the uncertainty of the date of death of any one individual. This study became the basis for the original <a href="/wiki/Life_table" title="Life table">life table</a>. One could now set up an insurance scheme to provide life insurance or pensions for a group of people, and to calculate with some degree of accuracy how much each person in the group should contribute to a common fund assumed to earn a fixed rate of interest. The first person to demonstrate publicly how this could be done was <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a> (of <a href="/wiki/Halley%27s_comet" class="mw-redirect" title="Halley's comet">Halley's comet</a> fame). Halley constructed his own life table, and showed how it could be used to calculate the <a href="/wiki/Insurance" title="Insurance">premium</a> amount someone of a given age should pay to purchase a life annuity.<sup id="cite_ref-FOOTNOTEHalley1693_20-0" class="reference"><a href="#cite_note-FOOTNOTEHalley1693-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Early_actuaries">Early actuaries</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=9" title="Edit section: Early actuaries"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/James_Dodson_(mathematician)" title="James Dodson (mathematician)">James Dodson</a>'s pioneering work on the long term insurance contracts under which the same premium is charged each year led to the formation of the Society for Equitable Assurances on Lives and Survivorship (now commonly known as <a href="/wiki/The_Equitable_Life_Assurance_Society" title="The Equitable Life Assurance Society">Equitable Life</a>) in London in 1762.<sup id="cite_ref-FOOTNOTELewin200738_21-0" class="reference"><a href="#cite_note-FOOTNOTELewin200738-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> <a href="/wiki/William_Morgan_(actuary)" title="William Morgan (actuary)">William Morgan</a> is often considered the father of modern actuarial science for his work in the field in the 1780s and 90s. Many other life insurance companies and pension funds were created over the following 200 years. Equitable Life was the first to use the word "actuary" for its chief executive officer in 1762.<sup id="cite_ref-FOOTNOTEOgborn1956235_22-0" class="reference"><a href="#cite_note-FOOTNOTEOgborn1956235-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Previously, "actuary" meant an official who recorded the decisions, or "acts", of ecclesiastical courts.<sup id="cite_ref-FOOTNOTEFaculty_and_Institute_of_Actuaries2004_19-1" class="reference"><a href="#cite_note-FOOTNOTEFaculty_and_Institute_of_Actuaries2004-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Other companies that did not use such mathematical and scientific methods most often failed or were forced to adopt the methods pioneered by Equitable.<sup id="cite_ref-FOOTNOTEBühlmann1997166_23-0" class="reference"><a href="#cite_note-FOOTNOTEBühlmann1997166-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Technological_advances">Technological advances</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=10" title="Edit section: Technological advances"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the 18th and 19th centuries, calculations were performed without computers. The computations of life insurance premiums and reserving requirements are rather complex, and actuaries developed techniques to make the calculations as easy as possible, for example "commutation functions" (essentially precalculated columns of summations over time of discounted values of survival and death probabilities).<sup id="cite_ref-FOOTNOTESlud2006_24-0" class="reference"><a href="#cite_note-FOOTNOTESlud2006-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Actuarial organizations were founded to support and further both actuaries and actuarial science, and to protect the public interest by promoting competency and ethical standards.<sup id="cite_ref-FOOTNOTEHickman20044_25-0" class="reference"><a href="#cite_note-FOOTNOTEHickman20044-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> However, calculations remained cumbersome, and actuarial shortcuts were commonplace. Non-life actuaries followed in the footsteps of their life insurance colleagues during the 20th century. The 1920 revision for the New-York based National Council on Workmen's Compensation Insurance rates took over two months of around-the-clock work by day and night teams of actuaries.<sup id="cite_ref-FOOTNOTEMichelbacher1920224,_230_26-0" class="reference"><a href="#cite_note-FOOTNOTEMichelbacher1920224,_230-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> In the 1930s and 1940s, the mathematical foundations for <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> processes were developed.<sup id="cite_ref-FOOTNOTEBühlmann1997168_27-0" class="reference"><a href="#cite_note-FOOTNOTEBühlmann1997168-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Actuaries could now begin to estimate losses using models of random events, instead of the <a href="/wiki/Deterministic" class="mw-redirect" title="Deterministic">deterministic</a> methods they had used in the past. The introduction and development of the computer further revolutionized the actuarial profession. From pencil-and-paper to punchcards to current high-speed devices, the modeling and forecasting ability of the actuary has rapidly improved, while still being heavily dependent on the assumptions input into the models, and actuaries needed to adjust to this new world .<sup id="cite_ref-FOOTNOTEMacGinnitie198050–51_28-0" class="reference"><a href="#cite_note-FOOTNOTEMacGinnitie198050–51-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Actuarial_control_cycle" title="Actuarial control cycle">Actuarial control cycle</a></li> <li><a href="/wiki/Actuarial_exam" class="mw-redirect" title="Actuarial exam">Actuarial exam</a></li> <li><a href="/wiki/Actuarial_notation" title="Actuarial notation">Actuarial notation</a></li> <li><a href="/wiki/Actuarial_present_value" title="Actuarial present value">Actuarial present value</a></li> <li><a href="/wiki/Black_swan_theory" title="Black swan theory">Black swan theory</a></li> <li><a href="/wiki/Category:Actuarial_associations" title="Category:Actuarial associations">Category:Actuarial associations</a></li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a></li> <li><a href="/wiki/List_of_actuarial_topics" class="mw-redirect" title="List of actuarial topics">List of actuarial topics</a></li> <li><a href="/wiki/Reinsurance_Actuarial_Premium" title="Reinsurance Actuarial Premium">Reinsurance Actuarial Premium</a></li> <li><a href="/wiki/Ruin_theory" title="Ruin theory">Ruin theory</a></li> <li><a href="/wiki/Scenario_optimization" title="Scenario optimization">Scenario optimization</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=12" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 22em;"> <ol class="references"> <li id="cite_note-FOOTNOTEFrees1990-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEFrees1990_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFFrees1990">Frees 1990</a>.</span> </li> <li id="cite_note-FOOTNOTENeedleman2010-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENeedleman2010_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNeedleman2010">Needleman 2010</a>.</span> </li> <li id="cite_note-FOOTNOTEU.S._News_&_World_Report2024-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEU.S._News_&_World_Report2024_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFU.S._News_&_World_Report2024">U.S. News & World Report 2024</a>.</span> </li> <li id="cite_note-FOOTNOTEHsiao2001-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHsiao2001_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHsiao2001">Hsiao 2001</a>.</span> </li> <li id="cite_note-FOOTNOTEHsiao2004-5"><span class="mw-cite-backlink"><b><a 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href="#CITEREFMacGinnitie1980">MacGinnitie 1980</a>, pp. 50–51.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Works_cited">Works cited</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=13" title="Edit section: Works cited"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 22em"> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBühlmann1997" class="citation journal cs1">Bühlmann, Hans (November 1997). <a rel="nofollow" class="external text" href="http://www.casact.org/library/astin/vol27no2/165.pdf">"The Actuary: the Role and Limitations of the Profession Since the Mid-19th Century"</a> <span class="cs1-format">(PDF)</span>. <i>ASTIN Bulletin</i>. <b>27</b> (2): 165–171. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a 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Revised November 19, 2004. California Health Benefits Review Program. February 9, 2004. Archived from <a rel="nofollow" class="external text" href="http://www.chbrp.org/documents/hearingaids174final.pdf">the original</a> <span class="cs1-format">(PDF)</span> on February 4, 2006<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-06-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Analysis+of+Senate+Bill+174%3A+Hearing+Aids+for+Children&rft.series=Revised+November+19%2C+2004&rft.pub=California+Health+Benefits+Review+Program&rft.date=2004-02-09&rft_id=http%3A%2F%2Fwww.chbrp.org%2Fdocuments%2Fhearingaids174final.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD'Arcy1989" class="citation journal cs1">D'Arcy, Stephen P. 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(December 1956). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120320062211/http://www.actuaries.org.uk/sites/all/files/documents/pdf/0233-0246.pdf">"The Professional Name of Actuary"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of the Institute of Actuaries</i>. <b>82</b> (2). Faculty and Institute of Actuaries: 233–246. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0020268100046424">10.1017/S0020268100046424</a>. Archived from <a rel="nofollow" class="external text" href="http://www.actuaries.org.uk/sites/all/files/documents/pdf/0233-0246.pdf">the original</a> <span class="cs1-format">(PDF)</span> on March 20, 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">April 27,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Institute+of+Actuaries&rft.atitle=The+Professional+Name+of+Actuary&rft.volume=82&rft.issue=2&rft.pages=233-246&rft.date=1956-12&rft_id=info%3Adoi%2F10.1017%2FS0020268100046424&rft.aulast=Ogborn&rft.aufirst=M.E.&rft_id=http%3A%2F%2Fwww.actuaries.org.uk%2Fsites%2Fall%2Ffiles%2Fdocuments%2Fpdf%2F0233-0246.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Perkins, Judith (August 25, 1995). <i>The Suffering Self; Pain and Narrative Representation in the Early Christian Era</i>. London: <a href="/wiki/Routledge" title="Routledge">Routledge</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-415-11363-6" title="Special:BookSources/0-415-11363-6"><bdi>0-415-11363-6</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/94042650">94042650</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Suffering+Self%3B+Pain+and+Narrative+Representation+in+the+Early+Christian+Era&rft.place=London&rft.pub=Routledge&rft.date=1995-08-25&rft_id=info%3Alccn%2F94042650&rft.isbn=0-415-11363-6&rft.aulast=Perkins&rft.aufirst=Judith&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilverChow-Martin2002" class="citation journal cs1">Silver, Eric; Chow-Martin, Lynette (October 2002). "A Multiple Models Approach To Assessing Recidivism Risk: Implications for Judicial Decision Making". <i>Criminal Justice and Behavior</i>. <b>29</b> (5): 538–568. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F009385402236732">10.1177/009385402236732</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0093-8548">0093-8548</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144800554">144800554</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Criminal+Justice+and+Behavior&rft.atitle=A+Multiple+Models+Approach+To+Assessing+Recidivism+Risk%3A+Implications+for+Judicial+Decision+Making&rft.volume=29&rft.issue=5&rft.pages=538-568&rft.date=2002-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144800554%23id-name%3DS2CID&rft.issn=0093-8548&rft_id=info%3Adoi%2F10.1177%2F009385402236732&rft.aulast=Silver&rft.aufirst=Eric&rft.au=Chow-Martin%2C+Lynette&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSlud2006" class="citation book cs1">Slud, Eric V. (2006) [2001]. <a rel="nofollow" class="external text" href="https://www.math.umd.edu/~evs/s470/BookChaps/Chp6.pdf">"6: Commutation Functions, Reserves & Select Mortality"</a> <span class="cs1-format">(PDF)</span>. <a rel="nofollow" class="external text" href="https://www.math.umd.edu/~evs/s470/BookChaps/01Book.pdf"><i>Actuarial Mathematics and Life-Table Statistics</i></a> <span class="cs1-format">(PDF)</span>. pp. 149–150<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-06-28</span></span>. <q><small>The Commutation Functions are a computational device to ensure that net single premiums...can all be obtained from a single table lookup. Historically, this idea has been very important in saving calculational labor when arriving at premium quotes. Even now...company employees without quantitative training could calculate premiums in a spreadsheet format with the aid of a life table.</small></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=6%3A+Commutation+Functions%2C+Reserves+%26+Select+Mortality&rft.btitle=Actuarial+Mathematics+and+Life-Table+Statistics&rft.pages=149-150&rft.date=2006&rft.aulast=Slud&rft.aufirst=Eric+V.&rft_id=https%3A%2F%2Fwww.math.umd.edu%2F~evs%2Fs470%2FBookChaps%2FChp6.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThucydides" class="citation book cs1"><a href="/wiki/Thucydides" title="Thucydides">Thucydides</a> (1994–2009) [c. 431 BCE]. <a rel="nofollow" class="external text" href="http://classics.mit.edu/Thucydides/pelopwar.2.second.html">"VI – Funeral Oration of Pericles"</a>. <a rel="nofollow" class="external text" href="http://classics.mit.edu/Thucydides/pelopwar.html"><i>History of the Peloponnesian War</i></a>. Translated by <a href="/wiki/Richard_Crawley" title="Richard Crawley">Richard Crawley</a>. <a href="/wiki/Greece" title="Greece">Greece</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2006-06-27</span></span>. <q><small>My task is now finished....those who are here interred have received part of their honours already, and for the rest, their children will be brought up till manhood at the public expense: the state thus offers a valuable prize, as the garland of victory in this race of valour, for the reward both of those who have fallen and their survivors.</small></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=VI+%E2%80%93+Funeral+Oration+of+Pericles&rft.btitle=History+of+the+Peloponnesian+War&rft.place=Greece&rft.date=1994%2F2009&rft.au=Thucydides&rft_id=http%3A%2F%2Fclassics.mit.edu%2FThucydides%2Fpelopwar.2.second.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1">Tong, Vinnee (June 19, 2006). <a rel="nofollow" class="external text" href="http://www.suntimes.com/output/news/cst-nws-phil19.html">"Americans' donations to charity near record"</a>. <i><a href="/wiki/Chicago_Sun-Times" title="Chicago Sun-Times">Chicago Sun-Times</a></i>. Digital Chicago Inc<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-06-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chicago+Sun-Times&rft.atitle=Americans%27+donations+to+charity+near+record&rft.date=2006-06-19&rft.aulast=Tong&rft.aufirst=Vinnee&rft_id=http%3A%2F%2Fwww.suntimes.com%2Foutput%2Fnews%2Fcst-nws-phil19.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFU.S._News_&_World_Report2024" class="citation web cs1"><a rel="nofollow" class="external text" href="https://money.usnews.com/careers/best-jobs/actuary">"Actuary Overview"</a>. <i><a href="/wiki/U.S._News_%26_World_Report" title="U.S. News & World Report">U.S. News & World Report</a></i>. 2024<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-08-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=U.S.+News+%26+World+Report&rft.atitle=Actuary+Overview&rft.date=2024&rft_id=https%3A%2F%2Fmoney.usnews.com%2Fcareers%2Fbest-jobs%2Factuary&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhelan2002" class="citation news cs1">Whelan, Shane (December 2002). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060724173342/http://www.the-actuary.org.uk/pdfs/02_12_08.pdf">"Actuaries' contributions to financial economics"</a> <span class="cs1-format">(PDF)</span>. <i>The Actuary</i>. Staple Inn Actuarial Society. pp. 34–35. Archived from <a rel="nofollow" class="external text" href="http://www.the-actuary.org.uk/pdfs/02_12_08.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2006-07-24<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-06-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Actuary&rft.atitle=Actuaries%27+contributions+to+financial+economics&rft.pages=34-35&rft.date=2002-12&rft.aulast=Whelan&rft.aufirst=Shane&rft_id=http%3A%2F%2Fwww.the-actuary.org.uk%2Fpdfs%2F02_12_08.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=14" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1">Charles L. Trowbridge (1989). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060629155610/http://www.actuarialfoundation.org/research_edu/fundamental.pdf">"Fundamental Concepts of Actuarial Science"</a> <span class="cs1-format">(PDF)</span>. Revised Edition. Actuarial Education and Research Fund. Archived from <a rel="nofollow" class="external text" href="http://www.actuarialfoundation.org/research_edu/fundamental.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2006-06-29<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-06-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Fundamental+Concepts+of+Actuarial+Science&rft.series=Revised+Edition&rft.pub=Actuarial+Education+and+Research+Fund&rft.date=1989&rft.au=Charles+L.+Trowbridge&rft_id=http%3A%2F%2Fwww.actuarialfoundation.org%2Fresearch_edu%2Ffundamental.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AActuarial+science" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Actuarial_science&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output 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class="navbox-group" style="width:1%"><a href="/wiki/Health_insurance" title="Health insurance">Health</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Accident_insurance" title="Accident insurance">Accident</a></li> <li><a href="/wiki/Accidental_death_and_dismemberment_insurance" title="Accidental death and dismemberment insurance">Accidental death and dismemberment</a></li> <li><a href="/wiki/Dental_insurance" title="Dental insurance">Dental</a></li> <li><a href="/wiki/Disability_insurance" title="Disability insurance">Disability</a> <ul><li><a href="/wiki/Total_permanent_disability_insurance" title="Total permanent disability insurance">Total permanent disability</a></li> <li><a href="/wiki/Business_overhead_expense_disability_insurance" title="Business overhead expense disability insurance">Business overhead expense</a></li></ul></li> <li><a href="/wiki/Income_protection_insurance" title="Income protection insurance">Income protection</a></li> <li><a href="/wiki/Long-term_care_insurance" title="Long-term care insurance">Long-term care</a></li> <li><a href="/wiki/National_health_insurance" title="National health insurance">National health</a></li> <li><a href="/wiki/Payment_protection_insurance" title="Payment protection insurance">Payment protection</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Life_insurance" title="Life insurance">Life</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Longevity_insurance" title="Longevity insurance">Longevity insurance</a></li> <li><a href="/wiki/Mortgage_life_insurance" title="Mortgage life insurance">Mortgage life</a></li> <li><a href="/wiki/Term_life_insurance" title="Term life insurance">Term life</a></li> <li><a href="/wiki/Unitised_insurance_fund" title="Unitised insurance fund">Unitised fund</a></li> <li><a href="/wiki/Universal_life_insurance" title="Universal life insurance">Universal life</a></li> <li><a href="/wiki/Variable_universal_life_insurance" title="Variable universal life insurance">Variable universal life</a></li> <li><a href="/wiki/Whole_life_insurance" title="Whole life insurance">Whole life</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Business</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bond_insurance" title="Bond insurance">Bond</a></li> <li><a href="/wiki/Business_interruption_insurance" title="Business interruption insurance">Business interruption</a></li> <li><a href="/wiki/Business_owner%27s_policy" title="Business owner's policy">Business owner</a></li> <li><a href="/wiki/Collateral_protection_insurance" title="Collateral protection insurance">Collateral protection</a></li> <li><a href="/wiki/Directors_and_officers_liability_insurance" title="Directors and officers liability insurance">Directors and officers liability</a></li> <li><a href="/wiki/Fidelity_bond" title="Fidelity bond">Fidelity</a></li> <li><a href="/wiki/Over-redemption_insurance" title="Over-redemption insurance">Over-redemption</a></li> <li><a href="/wiki/Payment_protection_insurance" title="Payment protection insurance">Payment protection</a></li> <li><a href="/wiki/Pollution_insurance" title="Pollution insurance">Pollution</a></li> <li><a href="/wiki/Professional_liability_insurance" title="Professional liability insurance">Professional liability</a></li> <li><a href="/wiki/Protection_and_indemnity_insurance" title="Protection and indemnity insurance">Protection and indemnity</a></li> <li><a href="/wiki/Surety" title="Surety">Surety</a></li> <li><a href="/wiki/Trade_credit_insurance" title="Trade credit insurance">Trade credit</a></li> <li><a href="/wiki/Umbrella_insurance" title="Umbrella insurance">Umbrella</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Residential</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boiler_insurance" class="mw-redirect" title="Boiler insurance">Boiler</a></li> <li><a href="/wiki/Builder%27s_risk_insurance" title="Builder's risk insurance">Builder's risk</a></li> <li><a href="/wiki/Contents_insurance" title="Contents insurance">Contents</a></li> <li><a href="/wiki/Earthquake_insurance" title="Earthquake insurance">Earthquake</a></li> <li><a href="/wiki/Flood_insurance" title="Flood insurance">Flood</a></li> <li><a href="/wiki/Home_insurance" title="Home insurance">Home</a></li> <li><a href="/wiki/Landlords%27_insurance" title="Landlords' insurance">Landlords'</a></li> <li><a href="/wiki/Lenders_mortgage_insurance" title="Lenders mortgage insurance">Lenders mortgage</a></li> <li><a href="/wiki/Mortgage_insurance" title="Mortgage insurance">Mortgage</a></li> <li><a href="/wiki/Property_insurance" title="Property insurance">Property</a></li> <li><a href="/wiki/Renters%27_insurance" title="Renters' insurance">Renters'</a></li> <li><a href="/wiki/Title_insurance" title="Title insurance">Title</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Transport/<br />Communication</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aviation_insurance" title="Aviation insurance">Aviation</a></li> <li><a href="/wiki/GAP_insurance" title="GAP insurance">GAP insurance</a></li> <li><a href="/wiki/Inland_marine_insurance" title="Inland marine insurance">Inland marine</a></li> <li><a href="/wiki/Public_auto_insurance" title="Public auto insurance">Public auto</a></li> <li><a href="/wiki/Marine_insurance" title="Marine insurance">Marine</a></li> <li><a href="/wiki/Satellite_insurance" title="Satellite insurance">Satellite</a></li> <li><a href="/wiki/Shipping_insurance" title="Shipping insurance">Shipping</a></li> <li><a href="/wiki/Travel_insurance" title="Travel insurance">Travel</a></li> <li><a href="/wiki/Vehicle_insurance" title="Vehicle insurance">Vehicle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Reinsurance" title="Reinsurance">Reinsurance</a> <ul><li><a href="/wiki/Catastrophe_bond" title="Catastrophe bond">Catastrophe bond</a></li> <li><a href="/wiki/Insurance-linked_security" title="Insurance-linked security">Insurance-linked securities</a></li></ul></li> <li><a href="/wiki/Casualty_insurance" title="Casualty insurance">Casualty</a></li> <li><a href="/wiki/Climate_risk_insurance" title="Climate risk insurance">Climate risk</a></li> <li><a href="/wiki/Insurance#Casualty_insurance" title="Insurance">Crime</a></li> <li><a href="/wiki/Crop_insurance" title="Crop insurance">Crop</a> <ul><li><a href="/wiki/Catastrophic_crop_insurance" title="Catastrophic crop insurance">Catastrophic</a></li> <li><a href="/wiki/Multi-peril_crop_insurance" title="Multi-peril crop insurance">Multi-peril</a></li></ul></li> <li><a href="/wiki/Cyber_insurance" title="Cyber insurance">Cyber</a></li> <li><a href="/wiki/Deposit_insurance" title="Deposit insurance">Deposit</a></li> <li><a href="/wiki/Expatriate_insurance" title="Expatriate insurance">Expatriate</a></li> <li><a href="/wiki/Extended_warranty" title="Extended warranty">Extended warranty</a></li> <li><a href="/wiki/Group_insurance" title="Group insurance">Group</a></li> <li><a href="/wiki/Index-based_insurance" title="Index-based insurance">Index-based</a> <ul><li><a href="/wiki/Parametric_insurance" title="Parametric insurance">Parametric</a></li></ul></li> <li><a href="/wiki/Interest_rate_insurance" title="Interest rate insurance">Interest rate</a></li> <li><a href="/wiki/Kidnap_and_ransom_insurance" title="Kidnap and ransom insurance">Kidnap and ransom</a></li> <li><a href="/wiki/Legal_expenses_insurance" title="Legal expenses insurance">Legal expenses</a></li> <li><a href="/wiki/Liability_insurance" title="Liability insurance">Liability</a></li> <li><a href="/wiki/No-fault_insurance" title="No-fault insurance">No-fault</a></li> <li><a href="/wiki/Pet_insurance" title="Pet insurance">Pet</a></li> <li><a href="/wiki/Political_risk_insurance" title="Political risk insurance">Political risk</a></li> <li><a href="/wiki/Prize_indemnity_insurance" title="Prize indemnity insurance">Prize indemnity</a></li> <li><a href="/wiki/Takaful" title="Takaful">Takaful</a></li> <li><a href="/wiki/Terrorism_insurance" title="Terrorism insurance">Terrorism</a></li> <li><a href="/wiki/Tuition_insurance" title="Tuition insurance">Tuition</a></li> <li><a href="/wiki/War_risk_insurance" title="War risk insurance">War risk</a></li> <li><a href="/wiki/Weather_insurance" title="Weather insurance">Weather</a></li> <li><a href="/wiki/Workers%27_compensation" title="Workers' compensation">Workers' compensation</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Insurance_policy" title="Insurance policy">Insurance <br />policy</a> <br />and <a href="/wiki/Insurance_law" title="Insurance law">law</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Act_of_God" title="Act of God">Act of God</a></li> <li><a class="mw-selflink selflink">Actuarial science</a> <ul><li><a href="/wiki/Actuary" title="Actuary">Actuary</a></li> <li><a href="/wiki/Adverse_selection" title="Adverse selection">Adverse selection</a></li> <li><a href="/wiki/Risk" title="Risk">Risk</a></li> <li><a href="/wiki/Risk_assessment" title="Risk assessment">Risk assessment</a></li> <li><a href="/wiki/Risk_management" title="Risk management">Risk management</a></li> <li><a href="/wiki/Uncertainty" title="Uncertainty">Uncertainty</a>/<a href="/wiki/Knightian_uncertainty" title="Knightian uncertainty">Knightian</a></li> <li><a href="/wiki/Value_of_life" title="Value of life">Value of life</a></li></ul></li> <li><a href="/wiki/Actual_cash_value" title="Actual cash value">Actual cash value</a></li> <li><a href="/wiki/Cash_value" title="Cash value">Cash value</a></li> <li><a href="/wiki/Insurance_broker" title="Insurance broker">Broker</a></li> <li><a href="/wiki/Cancellation_(insurance)" title="Cancellation (insurance)">Cancellation</a> <ul><li><i><a href="/wiki/Pro_rata" title="Pro rata">Pro rata</a></i></li> <li>Short rate table</li></ul></li> <li><a href="/wiki/Cause_of_action" title="Cause of action">Claim</a> <ul><li><a href="/wiki/Claims_adjuster" class="mw-redirect" title="Claims adjuster">Claims adjuster</a></li></ul></li> <li><a href="/wiki/Deductible" title="Deductible">Deductible</a> <ul><li><a href="/wiki/Co-insurance" title="Co-insurance">Co-insurance</a></li> <li><a href="/wiki/Copayment" title="Copayment">Copayment</a></li> <li><a href="/wiki/Out-of-pocket_expense" title="Out-of-pocket expense">Out-of-pocket expense</a></li></ul></li> <li><a href="/wiki/Explanation_of_benefits" title="Explanation of benefits">Explanation of benefits</a></li> <li><i><a href="/wiki/Force_majeure" title="Force majeure">Force majeure</a></i></li> <li><a href="/wiki/General_average" title="General average">General average</a></li> <li><a href="/wiki/Indemnity" title="Indemnity">Indemnity</a></li> <li><a href="/wiki/Insurability" title="Insurability">Insurability</a></li> <li><a href="/wiki/Insurable_interest" title="Insurable interest">Insurable interest</a></li> <li><a href="/wiki/Insurance_fraud" title="Insurance fraud">Insurance fraud</a></li> <li><a href="/wiki/Proximate_cause" title="Proximate cause">Proximate cause</a></li> <li><a href="/wiki/Replacement_value" title="Replacement value">Replacement value</a></li> <li><a href="/wiki/Risk_pool" title="Risk pool">Risk pool</a></li> <li><a href="/wiki/Self-insurance" title="Self-insurance">Self-insurance</a></li> <li><a href="/wiki/Total_loss" title="Total loss">Total loss</a></li> <li><a href="/wiki/Underinsured" title="Underinsured">Underinsurance</a></li> <li><a href="/wiki/Underwriting" title="Underwriting">Underwriting</a> <ul><li><a href="/wiki/Underwriting_profit" title="Underwriting profit">Profit</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Insurance <br />by country</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Insurance_in_Australia" title="Insurance in Australia">Australia</a></li> <li><a href="/wiki/Insurance_industry_in_China" title="Insurance industry in China">China</a></li> <li><a href="/wiki/Insurance_in_India" title="Insurance in India">India</a></li> <li><a href="/wiki/Insurance_in_Pakistan" title="Insurance in Pakistan">Pakistan</a></li> <li><a href="/wiki/Insurance_in_Serbia" title="Insurance in Serbia">Serbia</a></li> <li><a href="/wiki/Insurance_in_the_United_Kingdom" title="Insurance in the United Kingdom">United Kingdom</a></li> <li><a href="/wiki/Insurance_in_the_United_States" title="Insurance in the United States">United States</a> <ul><li><a href="/wiki/Climate_change_and_insurance_in_the_United_States" title="Climate change and insurance in the United States">Climate change</a></li> <li><a href="/wiki/Health_insurance_in_the_United_States" title="Health insurance in the United States">Health insurance</a></li> <li><a href="/wiki/Health_insurance_costs_in_the_United_States" title="Health insurance costs in the United States">Health insurance costs</a></li> <li><a href="/wiki/Health_insurance_coverage_in_the_United_States" title="Health insurance coverage in the United States">Health insurance coverage</a></li> <li><a href="/wiki/Vehicle_insurance_in_the_United_States" title="Vehicle insurance in the United States">Vehicle insurance</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_insurance" title="History of insurance">History</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Banker_(ancient)" title="Banker (ancient)">Mesopotamian banker</a></li> <li><a href="/wiki/Code_of_Hammurabi" title="Code of Hammurabi">Code of Hammurabi</a> <ul><li><a href="/wiki/Marine_insurance" title="Marine insurance">§100–105; §126</a>; <a href="/wiki/Labour_law" title="Labour law">§234</a>; <a href="/wiki/Marine_insurance" title="Marine insurance">§235–238; §240</a>; <a href="/wiki/Labour_law" title="Labour law">§275–277</a></li></ul></li> <li><i><a href="/wiki/Collegium_(ancient_Rome)" title="Collegium (ancient Rome)">Collegium</a></i> <ul><li><a href="/wiki/Burial_society" title="Burial society">Burial society</a></li> <li><a href="/wiki/Guild" title="Guild">Guild</a></li></ul></li> <li><i><a href="/wiki/Corpus_Juris_Civilis" title="Corpus Juris Civilis">Corpus Juris Civilis</a></i> <ul><li><i><a href="/wiki/Digest_(Roman_law)" title="Digest (Roman law)">Digesta</a></i></li></ul></li> <li><a href="/wiki/Syndicate" title="Syndicate">Syndicate</a></li> <li><a href="/wiki/Benefit_society" title="Benefit society">Benefit</a>/<a href="/wiki/Friendly_society" title="Friendly society">Friendly society</a> <ul><li><a href="/wiki/Cooperative" title="Cooperative">Cooperative</a></li> <li><a href="/wiki/Cooperative_banking" title="Cooperative banking">Cooperative banking</a></li> <li><a href="/wiki/Credit_union" title="Credit union">Credit union</a></li> <li><a href="/wiki/Fraternal_order" title="Fraternal order">Fraternal order</a></li> <li><a href="/wiki/Mutual_organization" title="Mutual organization">Mutual organization</a></li> <li><a href="/wiki/Mutual_savings_bank" title="Mutual savings bank">Mutual savings bank</a></li> <li><a href="/wiki/Rochdale_Principles" title="Rochdale Principles">Rochdale Principles</a></li> <li><a href="/wiki/Savings_and_loan_association" title="Savings and loan association">Savings and loan association</a></li> <li><a href="/wiki/Social_insurance" title="Social insurance">Social insurance</a></li> <li><a href="/wiki/Trade_union" title="Trade union">Trade union</a></li></ul></li> <li><a href="/wiki/Insurance_cycle" title="Insurance cycle">Insurance cycle</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><b><a href="/wiki/Category:Insurance" title="Category:Insurance">Category</a></b></li> <li><b><a href="/wiki/Outline_of_finance#Insurance" title="Outline of finance">List of topics</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Statistics" style="padding:3px"><table class="nowraplinks hlist mw-collapsible uncollapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Statistics" title="Template:Statistics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Statistics" title="Template talk:Statistics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Statistics" title="Special:EditPage/Template:Statistics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Statistics" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistics" title="Statistics">Statistics</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline</a></li> <li><a href="/wiki/List_of_statistics_articles" title="List of statistics articles">Index</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Descriptive_statistics" style="font-size:114%;margin:0 4em"><a href="/wiki/Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">Continuous data</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Central_tendency" title="Central tendency">Center</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mean" title="Mean">Mean</a> <ul><li><a href="/wiki/Arithmetic_mean" title="Arithmetic mean">Arithmetic</a></li> <li><a href="/wiki/Arithmetic%E2%80%93geometric_mean" title="Arithmetic–geometric mean">Arithmetic-Geometric</a></li> <li><a href="/wiki/Contraharmonic_mean" title="Contraharmonic mean">Contraharmonic</a></li> <li><a href="/wiki/Cubic_mean" title="Cubic mean">Cubic</a></li> <li><a href="/wiki/Generalized_mean" title="Generalized mean">Generalized/power</a></li> <li><a href="/wiki/Geometric_mean" title="Geometric mean">Geometric</a></li> <li><a href="/wiki/Harmonic_mean" title="Harmonic mean">Harmonic</a></li> <li><a href="/wiki/Heronian_mean" title="Heronian mean">Heronian</a></li> <li><a href="/wiki/Heinz_mean" title="Heinz mean">Heinz</a></li> <li><a href="/wiki/Lehmer_mean" title="Lehmer mean">Lehmer</a></li></ul></li> <li><a href="/wiki/Median" title="Median">Median</a></li> <li><a href="/wiki/Mode_(statistics)" title="Mode (statistics)">Mode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_dispersion" title="Statistical dispersion">Dispersion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Average_absolute_deviation" title="Average absolute deviation">Average absolute deviation</a></li> <li><a href="/wiki/Coefficient_of_variation" title="Coefficient of variation">Coefficient of variation</a></li> <li><a href="/wiki/Interquartile_range" title="Interquartile range">Interquartile range</a></li> <li><a href="/wiki/Percentile" title="Percentile">Percentile</a></li> <li><a href="/wiki/Range_(statistics)" title="Range (statistics)">Range</a></li> <li><a href="/wiki/Standard_deviation" title="Standard deviation">Standard deviation</a></li> <li><a href="/wiki/Variance#Sample_variance" title="Variance">Variance</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Shape_of_the_distribution" class="mw-redirect" title="Shape of the distribution">Shape</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Central_limit_theorem" title="Central limit theorem">Central limit theorem</a></li> <li><a href="/wiki/Moment_(mathematics)" title="Moment (mathematics)">Moments</a> <ul><li><a href="/wiki/Kurtosis" title="Kurtosis">Kurtosis</a></li> <li><a href="/wiki/L-moment" title="L-moment">L-moments</a></li> <li><a href="/wiki/Skewness" title="Skewness">Skewness</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Count_data" title="Count data">Count data</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Summary tables</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li> <li><a href="/wiki/Grouped_data" title="Grouped data">Grouped data</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Dependence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Pearson_correlation_coefficient" title="Pearson correlation coefficient">Pearson product-moment correlation</a></li> <li><a href="/wiki/Rank_correlation" title="Rank correlation">Rank correlation</a> <ul><li><a href="/wiki/Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Kendall's τ</a></li> <li><a href="/wiki/Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's ρ</a></li></ul></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_graphics" title="Statistical graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bar_chart" title="Bar chart">Bar chart</a></li> <li><a href="/wiki/Biplot" title="Biplot">Biplot</a></li> <li><a href="/wiki/Box_plot" title="Box plot">Box plot</a></li> <li><a href="/wiki/Control_chart" title="Control chart">Control chart</a></li> <li><a href="/wiki/Correlogram" title="Correlogram">Correlogram</a></li> <li><a href="/wiki/Fan_chart_(statistics)" title="Fan chart (statistics)">Fan chart</a></li> <li><a href="/wiki/Forest_plot" title="Forest plot">Forest plot</a></li> <li><a href="/wiki/Histogram" title="Histogram">Histogram</a></li> <li><a href="/wiki/Pie_chart" title="Pie chart">Pie chart</a></li> <li><a href="/wiki/Q%E2%80%93Q_plot" title="Q–Q plot">Q–Q plot</a></li> <li><a href="/wiki/Radar_chart" title="Radar chart">Radar chart</a></li> <li><a href="/wiki/Run_chart" title="Run chart">Run chart</a></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li> <li><a href="/wiki/Stem-and-leaf_display" title="Stem-and-leaf display">Stem-and-leaf display</a></li> <li><a href="/wiki/Violin_plot" title="Violin plot">Violin plot</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_collection" style="font-size:114%;margin:0 4em"><a href="/wiki/Data_collection" title="Data collection">Data collection</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Design_of_experiments" title="Design of experiments">Study design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Effect_size" title="Effect size">Effect size</a></li> <li><a href="/wiki/Missing_data" title="Missing data">Missing data</a></li> <li><a href="/wiki/Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></li> <li><a href="/wiki/Statistical_population" title="Statistical population">Population</a></li> <li><a href="/wiki/Replication_(statistics)" title="Replication (statistics)">Replication</a></li> <li><a href="/wiki/Sample_size_determination" title="Sample size determination">Sample size determination</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">Statistical power</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survey_methodology" title="Survey methodology">Survey methodology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">Sampling</a> <ul><li><a href="/wiki/Cluster_sampling" title="Cluster sampling">Cluster</a></li> <li><a href="/wiki/Stratified_sampling" title="Stratified sampling">Stratified</a></li></ul></li> <li><a href="/wiki/Opinion_poll" title="Opinion poll">Opinion poll</a></li> <li><a href="/wiki/Questionnaire" title="Questionnaire">Questionnaire</a></li> <li><a href="/wiki/Standard_error" title="Standard error">Standard error</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Experiment" title="Experiment">Controlled experiments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li> <li><a href="/wiki/Factorial_experiment" title="Factorial experiment">Factorial experiment</a></li> <li><a href="/wiki/Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li> <li><a href="/wiki/Random_assignment" title="Random assignment">Random assignment</a></li> <li><a href="/wiki/Randomized_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</a></li> <li><a href="/wiki/Randomized_experiment" title="Randomized experiment">Randomized experiment</a></li> <li><a href="/wiki/Scientific_control" title="Scientific control">Scientific control</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Adaptive designs</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li> <li><a href="/wiki/Stochastic_approximation" title="Stochastic approximation">Stochastic approximation</a></li> <li><a href="/wiki/Up-and-Down_Designs" class="mw-redirect" title="Up-and-Down Designs">Up-and-down designs</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Observational_study" title="Observational study">Observational studies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohort_study" title="Cohort study">Cohort study</a></li> <li><a href="/wiki/Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a></li> <li><a href="/wiki/Natural_experiment" title="Natural experiment">Natural experiment</a></li> <li><a href="/wiki/Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_inference" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistical_inference" title="Statistical inference">Statistical inference</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_theory" title="Statistical theory">Statistical theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Population_(statistics)" class="mw-redirect" title="Population (statistics)">Population</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Probability_distribution" title="Probability distribution">Probability distribution</a></li> <li><a href="/wiki/Sampling_distribution" title="Sampling distribution">Sampling distribution</a> <ul><li><a href="/wiki/Order_statistic" title="Order statistic">Order statistic</a></li></ul></li> <li><a href="/wiki/Empirical_distribution_function" title="Empirical distribution function">Empirical distribution</a> <ul><li><a href="/wiki/Density_estimation" title="Density estimation">Density estimation</a></li></ul></li> <li><a href="/wiki/Statistical_model" title="Statistical model">Statistical model</a> <ul><li><a href="/wiki/Model_specification" class="mw-redirect" title="Model specification">Model specification</a></li> <li><a href="/wiki/Lp_space" title="Lp space">L<sup><i>p</i></sup> space</a></li></ul></li> <li><a href="/wiki/Statistical_parameter" title="Statistical parameter">Parameter</a> <ul><li><a href="/wiki/Location_parameter" title="Location parameter">location</a></li> <li><a href="/wiki/Scale_parameter" title="Scale parameter">scale</a></li> <li><a href="/wiki/Shape_parameter" title="Shape parameter">shape</a></li></ul></li> <li><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric family</a> <ul><li><a href="/wiki/Likelihood_function" title="Likelihood function">Likelihood</a> <a href="/wiki/Monotone_likelihood_ratio" title="Monotone likelihood ratio"><span style="font-size:85%;">(monotone)</span></a></li> <li><a href="/wiki/Location%E2%80%93scale_family" title="Location–scale family">Location–scale family</a></li> <li><a href="/wiki/Exponential_family" title="Exponential family">Exponential family</a></li></ul></li> <li><a href="/wiki/Completeness_(statistics)" title="Completeness (statistics)">Completeness</a></li> <li><a href="/wiki/Sufficient_statistic" title="Sufficient statistic">Sufficiency</a></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Statistical functional</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/U-statistic" title="U-statistic">U</a></li> <li><a href="/wiki/V-statistic" title="V-statistic">V</a></li></ul></li> <li><a href="/wiki/Optimal_decision" title="Optimal decision">Optimal decision</a> <ul><li><a href="/wiki/Loss_function" title="Loss function">loss function</a></li></ul></li> <li><a href="/wiki/Efficiency_(statistics)" title="Efficiency (statistics)">Efficiency</a></li> <li><a href="/wiki/Statistical_distance" title="Statistical distance">Statistical distance</a> <ul><li><a href="/wiki/Divergence_(statistics)" title="Divergence (statistics)">divergence</a></li></ul></li> <li><a href="/wiki/Asymptotic_theory_(statistics)" title="Asymptotic theory (statistics)">Asymptotics</a></li> <li><a href="/wiki/Robust_statistics" title="Robust statistics">Robustness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Frequentist_inference" title="Frequentist inference">Frequentist inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Point_estimation" title="Point estimation">Point estimation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Estimating_equations" title="Estimating equations">Estimating equations</a> <ul><li><a href="/wiki/Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">Maximum likelihood</a></li> <li><a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">Method of moments</a></li> <li><a href="/wiki/M-estimator" title="M-estimator">M-estimator</a></li> <li><a href="/wiki/Minimum_distance_estimation" class="mw-redirect" title="Minimum distance estimation">Minimum distance</a></li></ul></li> <li><a href="/wiki/Bias_of_an_estimator" title="Bias of an estimator">Unbiased estimators</a> <ul><li><a href="/wiki/Minimum-variance_unbiased_estimator" title="Minimum-variance unbiased estimator">Mean-unbiased minimum-variance</a> <ul><li><a href="/wiki/Rao%E2%80%93Blackwell_theorem" title="Rao–Blackwell theorem">Rao–Blackwellization</a></li> <li><a href="/wiki/Lehmann%E2%80%93Scheff%C3%A9_theorem" title="Lehmann–Scheffé theorem">Lehmann–Scheffé theorem</a></li></ul></li> <li><a href="/wiki/Median-unbiased_estimator" class="mw-redirect" title="Median-unbiased estimator">Median unbiased</a></li></ul></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Plug-in</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Interval_estimation" title="Interval estimation">Interval estimation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Confidence_interval" title="Confidence interval">Confidence interval</a></li> <li><a href="/wiki/Pivotal_quantity" title="Pivotal quantity">Pivot</a></li> <li><a href="/wiki/Likelihood_interval" class="mw-redirect" title="Likelihood interval">Likelihood interval</a></li> <li><a href="/wiki/Prediction_interval" title="Prediction interval">Prediction interval</a></li> <li><a href="/wiki/Tolerance_interval" title="Tolerance interval">Tolerance interval</a></li> <li><a href="/wiki/Resampling_(statistics)" title="Resampling (statistics)">Resampling</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/Jackknife_resampling" title="Jackknife resampling">Jackknife</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Testing hypotheses</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/One-_and_two-tailed_tests" title="One- and two-tailed tests">1- & 2-tails</a></li> <li><a href="/wiki/Power_(statistics)" title="Power (statistics)">Power</a> <ul><li><a href="/wiki/Uniformly_most_powerful_test" title="Uniformly most powerful test">Uniformly most powerful test</a></li></ul></li> <li><a href="/wiki/Permutation_test" title="Permutation test">Permutation test</a> <ul><li><a href="/wiki/Randomization_test" class="mw-redirect" title="Randomization test">Randomization test</a></li></ul></li> <li><a href="/wiki/Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">Multiple comparisons</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio</a></li> <li><a href="/wiki/Score_test" title="Score test">Score/Lagrange multiplier</a></li> <li><a href="/wiki/Wald_test" title="Wald test">Wald</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/List_of_statistical_tests" title="List of statistical tests">Specific tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Z-test" title="Z-test"><i>Z</i>-test <span style="font-size:85%;">(normal)</span></a></li> <li><a href="/wiki/Student%27s_t-test" title="Student's t-test">Student's <i>t</i>-test</a></li> <li><a href="/wiki/F-test" title="F-test"><i>F</i>-test</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Goodness_of_fit" title="Goodness of fit">Goodness of fit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chi-squared_test" title="Chi-squared test">Chi-squared</a></li> <li><a href="/wiki/G-test" title="G-test"><i>G</i>-test</a></li> <li><a href="/wiki/Kolmogorov%E2%80%93Smirnov_test" title="Kolmogorov–Smirnov test">Kolmogorov–Smirnov</a></li> <li><a href="/wiki/Anderson%E2%80%93Darling_test" title="Anderson–Darling test">Anderson–Darling</a></li> <li><a href="/wiki/Lilliefors_test" title="Lilliefors test">Lilliefors</a></li> <li><a href="/wiki/Jarque%E2%80%93Bera_test" title="Jarque–Bera test">Jarque–Bera</a></li> <li><a href="/wiki/Shapiro%E2%80%93Wilk_test" title="Shapiro–Wilk test">Normality <span style="font-size:85%;">(Shapiro–Wilk)</span></a></li> <li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio test</a></li> <li><a href="/wiki/Model_selection" title="Model selection">Model selection</a> <ul><li><a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross validation</a></li> <li><a href="/wiki/Akaike_information_criterion" title="Akaike information criterion">AIC</a></li> <li><a href="/wiki/Bayesian_information_criterion" title="Bayesian information criterion">BIC</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Rank_statistics" class="mw-redirect" title="Rank statistics">Rank statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sign_test" title="Sign test">Sign</a> <ul><li><a href="/wiki/Sample_median" class="mw-redirect" title="Sample median">Sample median</a></li></ul></li> <li><a href="/wiki/Wilcoxon_signed-rank_test" title="Wilcoxon signed-rank test">Signed rank <span style="font-size:85%;">(Wilcoxon)</span></a> <ul><li><a href="/wiki/Hodges%E2%80%93Lehmann_estimator" title="Hodges–Lehmann estimator">Hodges–Lehmann estimator</a></li></ul></li> <li><a href="/wiki/Mann%E2%80%93Whitney_U_test" title="Mann–Whitney U test">Rank sum <span style="font-size:85%;">(Mann–Whitney)</span></a></li> <li><a href="/wiki/Nonparametric_statistics" title="Nonparametric statistics">Nonparametric</a> <a href="/wiki/Analysis_of_variance" title="Analysis of variance">anova</a> <ul><li><a href="/wiki/Kruskal%E2%80%93Wallis_test" title="Kruskal–Wallis test">1-way <span style="font-size:85%;">(Kruskal–Wallis)</span></a></li> <li><a href="/wiki/Friedman_test" title="Friedman test">2-way <span style="font-size:85%;">(Friedman)</span></a></li> <li><a href="/wiki/Jonckheere%27s_trend_test" title="Jonckheere's trend test">Ordered alternative <span style="font-size:85%;">(Jonckheere–Terpstra)</span></a></li></ul></li> <li><a href="/wiki/Van_der_Waerden_test" title="Van der Waerden test">Van der Waerden test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bayesian_probability" title="Bayesian probability">Bayesian probability</a> <ul><li><a href="/wiki/Prior_probability" title="Prior probability">prior</a></li> <li><a href="/wiki/Posterior_probability" title="Posterior probability">posterior</a></li></ul></li> <li><a href="/wiki/Credible_interval" title="Credible interval">Credible interval</a></li> <li><a href="/wiki/Bayes_factor" title="Bayes factor">Bayes factor</a></li> <li><a href="/wiki/Bayes_estimator" title="Bayes estimator">Bayesian estimator</a> <ul><li><a href="/wiki/Maximum_a_posteriori_estimation" title="Maximum a posteriori estimation">Maximum posterior estimator</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="CorrelationRegression_analysis" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></li><li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment</a></li> <li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Confounding" title="Confounding">Confounding variable</a></li> <li><a href="/wiki/Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Errors_and_residuals" title="Errors and residuals">Errors and residuals</a></li> <li><a href="/wiki/Regression_validation" title="Regression validation">Regression validation</a></li> <li><a href="/wiki/Mixed_model" title="Mixed model">Mixed effects models</a></li> <li><a href="/wiki/Simultaneous_equations_model" title="Simultaneous equations model">Simultaneous equations models</a></li> <li><a href="/wiki/Multivariate_adaptive_regression_splines" class="mw-redirect" title="Multivariate adaptive regression splines">Multivariate adaptive regression splines (MARS)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Linear_regression" title="Linear regression">Linear regression</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Simple_linear_regression" title="Simple linear regression">Simple linear regression</a></li> <li><a href="/wiki/Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li> <li><a href="/wiki/General_linear_model" title="General linear model">General linear model</a></li> <li><a href="/wiki/Bayesian_linear_regression" title="Bayesian linear regression">Bayesian regression</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Non-standard predictors</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonlinear_regression" title="Nonlinear regression">Nonlinear regression</a></li> <li><a href="/wiki/Nonparametric_regression" title="Nonparametric regression">Nonparametric</a></li> <li><a href="/wiki/Semiparametric_regression" title="Semiparametric regression">Semiparametric</a></li> <li><a href="/wiki/Isotonic_regression" title="Isotonic regression">Isotonic</a></li> <li><a href="/wiki/Robust_regression" title="Robust regression">Robust</a></li> <li><a href="/wiki/Heteroscedasticity" class="mw-redirect" title="Heteroscedasticity">Heteroscedasticity</a></li> <li><a href="/wiki/Homoscedasticity" class="mw-redirect" title="Homoscedasticity">Homoscedasticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Generalized_linear_model" title="Generalized linear model">Generalized linear model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Exponential_family" title="Exponential family">Exponential families</a></li> <li><a href="/wiki/Logistic_regression" title="Logistic regression">Logistic <span style="font-size:85%;">(Bernoulli)</span></a> / <a href="/wiki/Binomial_regression" title="Binomial regression">Binomial</a> / <a href="/wiki/Poisson_regression" title="Poisson regression">Poisson regressions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Partition_of_sums_of_squares" title="Partition of sums of squares">Partition of variance</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA, anova)</a></li> <li><a href="/wiki/Analysis_of_covariance" title="Analysis of covariance">Analysis of covariance</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate ANOVA</a></li> <li><a href="/wiki/Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">Degrees of freedom</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Categorical_/_Multivariate_/_Time-series_/_Survival_analysis" style="font-size:114%;margin:0 4em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a> / <a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a> / <a href="/wiki/Time_series" title="Time series">Time-series</a> / <a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohen%27s_kappa" title="Cohen's kappa">Cohen's kappa</a></li> <li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Graphical_model" title="Graphical model">Graphical model</a></li> <li><a href="/wiki/Poisson_regression" title="Poisson regression">Log-linear model</a></li> <li><a href="/wiki/McNemar%27s_test" title="McNemar's test">McNemar's test</a></li> <li><a href="/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics" title="Cochran–Mantel–Haenszel statistics">Cochran–Mantel–Haenszel statistics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_linear_model" title="General linear model">Regression</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova</a></li> <li><a href="/wiki/Principal_component_analysis" title="Principal component analysis">Principal components</a></li> <li><a href="/wiki/Canonical_correlation" title="Canonical correlation">Canonical correlation</a></li> <li><a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">Discriminant analysis</a></li> <li><a href="/wiki/Cluster_analysis" title="Cluster analysis">Cluster analysis</a></li> <li><a href="/wiki/Statistical_classification" title="Statistical classification">Classification</a></li> <li><a href="/wiki/Structural_equation_modeling" title="Structural equation modeling">Structural equation model</a> <ul><li><a href="/wiki/Factor_analysis" title="Factor analysis">Factor analysis</a></li></ul></li> <li><a href="/wiki/Multivariate_distribution" class="mw-redirect" title="Multivariate distribution">Multivariate distributions</a> <ul><li><a href="/wiki/Elliptical_distribution" title="Elliptical distribution">Elliptical distributions</a> <ul><li><a href="/wiki/Multivariate_normal_distribution" title="Multivariate normal distribution">Normal</a></li></ul></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Time_series" title="Time series">Time-series</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Decomposition_of_time_series" title="Decomposition of time series">Decomposition</a></li> <li><a href="/wiki/Trend_estimation" class="mw-redirect" title="Trend estimation">Trend</a></li> <li><a href="/wiki/Stationary_process" title="Stationary process">Stationarity</a></li> <li><a href="/wiki/Seasonal_adjustment" title="Seasonal adjustment">Seasonal adjustment</a></li> <li><a href="/wiki/Exponential_smoothing" title="Exponential smoothing">Exponential smoothing</a></li> <li><a href="/wiki/Cointegration" title="Cointegration">Cointegration</a></li> <li><a href="/wiki/Structural_break" title="Structural break">Structural break</a></li> <li><a href="/wiki/Granger_causality" title="Granger causality">Granger causality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Specific tests</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dickey%E2%80%93Fuller_test" title="Dickey–Fuller test">Dickey–Fuller</a></li> <li><a href="/wiki/Johansen_test" title="Johansen test">Johansen</a></li> <li><a href="/wiki/Ljung%E2%80%93Box_test" title="Ljung–Box test">Q-statistic <span style="font-size:85%;">(Ljung–Box)</span></a></li> <li><a href="/wiki/Durbin%E2%80%93Watson_statistic" title="Durbin–Watson statistic">Durbin–Watson</a></li> <li><a href="/wiki/Breusch%E2%80%93Godfrey_test" title="Breusch–Godfrey test">Breusch–Godfrey</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Time_domain" title="Time domain">Time domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autocorrelation" title="Autocorrelation">Autocorrelation (ACF)</a> <ul><li><a href="/wiki/Partial_autocorrelation_function" title="Partial autocorrelation function">partial (PACF)</a></li></ul></li> <li><a href="/wiki/Cross-correlation" title="Cross-correlation">Cross-correlation (XCF)</a></li> <li><a href="/wiki/Autoregressive%E2%80%93moving-average_model" class="mw-redirect" title="Autoregressive–moving-average model">ARMA model</a></li> <li><a href="/wiki/Box%E2%80%93Jenkins_method" title="Box–Jenkins method">ARIMA model <span style="font-size:85%;">(Box–Jenkins)</span></a></li> <li><a href="/wiki/Autoregressive_conditional_heteroskedasticity" title="Autoregressive conditional heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li> <li><a href="/wiki/Vector_autoregression" title="Vector autoregression">Vector autoregression (VAR)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Frequency_domain" title="Frequency domain">Frequency domain</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Spectral_density_estimation" title="Spectral density estimation">Spectral density estimation</a></li> <li><a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li> <li><a href="/wiki/Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li> <li><a href="/wiki/Wavelet" title="Wavelet">Wavelet</a></li> <li><a href="/wiki/Whittle_likelihood" title="Whittle likelihood">Whittle likelihood</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survival_analysis" title="Survival analysis">Survival</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Survival_function" title="Survival function">Survival function</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimator (product limit)</a></li> <li><a href="/wiki/Proportional_hazards_model" title="Proportional hazards model">Proportional hazards models</a></li> <li><a href="/wiki/Accelerated_failure_time_model" title="Accelerated failure time model">Accelerated failure time (AFT) model</a></li> <li><a href="/wiki/First-hitting-time_model" title="First-hitting-time model">First hitting time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Failure_rate" title="Failure rate">Hazard function</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nelson%E2%80%93Aalen_estimator" title="Nelson–Aalen estimator">Nelson–Aalen estimator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Test</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Log-rank_test" class="mw-redirect" title="Log-rank test">Log-rank test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" 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