Document Zbl 1154.62340

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J. Math. Manage. Sci.</a> <a href="/?q=in%3A219228" title="Articles in this Issue">27, No. 3-4, Spec. Iss., 351-368 (2007)</a>. </div> <div class="abstract">Summary: A new bivariate beta distribution based on the Appell function of the second kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix. Finally, an application to drought data from Nebraska is illustrated.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5507289">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H10" title="MSC2020">62H10</a> </td> <td class="space"> Multivariate distribution of statistics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A33C90" title="MSC2020">33C90</a> </td> <td class="space"> Applications of hypergeometric functions </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H12" title="MSC2020">62H12</a> </td> <td class="space"> Estimation in multivariate analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H05" title="MSC2020">62H05</a> </td> <td class="space"> Characterization and structure theory for multivariate probability distributions; copulas </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P12" title="MSC2020">62P12</a> </td> <td class="space"> Applications of statistics to environmental and related topics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AAppel+function+of+the+second+kind">Appel function of the second kind</a>; <a href="/?q=ut%3Abivariate+beta+distribution">bivariate beta distribution</a>; <a href="/?q=ut%3Adrought+data">drought data</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1154.62340" data-ciurl="/ci/05507289" data-biburl="/bibtex/05507289.bib" data-amsurl="/amsrefs/05507289.bib" data-xmlurl="/xml/05507289.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05507289.pdf" title="Zbl 1154.62340 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1080/01966324.2007.10737705" aria-label="DOI for “The bivariate $F_2$-beta distribution”" title="10.1080/01966324.2007.10737705">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A-Grivas D., Journal of the Geotechnical Engineering Division, Proceedings of the American Society of Civil Engineers 108 pp 713– (1982)</td> </tr><tr> <td>[2]</td> <td class="space">Apostolakis G., Reliability Engineering 18 pp 177– (1987) · <a href="https://doi.org/10.1016/0143-8174(87)90097-7" class="nowrap">doi:10.1016/0143-8174(87)90097-7</a></td> </tr><tr> <td>[3]</td> <td class="space">Arnold B. C., Conditional Specification of Statistical Models. (1999) · <a href="/0932.62001" class="nowrap">Zbl 0932.62001</a></td> </tr><tr> <td>[4]</td> <td class="space">Chatfield C., A Modem Course on Distributions in Scientific Work, volume 2: Model Building and Model Selection pp 175– (1975) · <a href="https://doi.org/10.1007/978-94-010-1845-6_15" class="nowrap">doi:10.1007/978-94-010-1845-6_15</a></td> </tr><tr> <td>[5]</td> <td class="space">Hoyer R. W., The equivalence of various objective functions in a stochastic model of electoral competition (1976)</td> </tr><tr> <td>[6]</td> <td class="space">Hutchinson T. P., The Engineering Statistician’s Guide to Continuous Bivariate Distributions. (1991)</td> </tr><tr> <td>[7]</td> <td class="space">Libby D. L., Journal of Educational Statistics 7 pp 271– (1982) · <a href="https://doi.org/10.2307/1164635" class="nowrap">doi:10.2307/1164635</a></td> </tr><tr> <td>[8]</td> <td class="space">Kotz S., Continuous Multivariate Distributions, volume 1: Models and Applications (2000) · <a href="/0946.62001" class="nowrap">Zbl 0946.62001</a> · <a href="https://doi.org/10.1002/0471722065" class="nowrap">doi:10.1002/0471722065</a></td> </tr><tr> <td>[9]</td> <td class="space">Olkin I., Statistics and Probability Letters 62 pp 407– (2003) · <a href="/1116.60309" class="nowrap">Zbl 1116.60309</a> · <a href="https://doi.org/10.1016/S0167-7152(03)00048-8" class="nowrap">doi:10.1016/S0167-7152(03)00048-8</a></td> </tr><tr> <td>[10]</td> <td class="space">Prudnikov A. P., Integrals and Series 1 (1986) · <a href="/0606.33001" class="nowrap">Zbl 0606.33001</a></td> </tr><tr> <td>[11]</td> <td class="space">Yevjevich V., An objective approach to definitions and investigations of continental hydrologic droughts (1967)</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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