Document Zbl 1519.94015

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Comput. Appl. Probab.</a> <a href="/?q=in%3A499330" title="Articles in this Issue">25, No. 2, Paper No. 61, 23 p. (2023)</a>. </div> <div class="abstract">Let $K$ be the cumulative distribution function of a random variable $X$ with support $(0,s)$. The authors define the weighted fractional generalized cumulative past entropy (WFGCPE) with $\operatorname{CPE}_\gamma ^\psi (X) = \frac{1}{{\Gamma (\gamma + 1)}}\int_0^s {\psi (x)K(x){{[ - \ln K(x)]}^\gamma }dx} $, $\gamma > 0$, derive for it some bounds and stochastic orders, show connection of the proposed measure with the left-sided Riemann-Liouville fractional integral, consider it for the proportional reversed hazard rate model and propose a nonparametric estimator based on an empirical distribution function. The empirical estimator of WFGCPE is compared with the standard deviation and Gini’s mean difference for exponential distribution using stock prices in Japan (225), USA (Nashdaq), India (Nifty50), and France (Cac40) during the Russia-Ukraine war using data from “<a href="https://finance.yahoo.com/">https://finance.yahoo.com/</a>”.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A3541">Jaak Henno (Tallinn)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7716609">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A94A17" title="MSC2020">94A17</a> </td> <td class="space"> Measures of information, entropy </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60E15" title="MSC2020">60E15</a> </td> <td class="space"> Inequalities; stochastic orderings </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aweighted+generalized+cumulative+past+entropy">weighted generalized cumulative past entropy</a>; <a href="/?q=ut%3Afractional+calculus">fractional calculus</a>; <a href="/?q=ut%3Areversed+hazard+rate+model">reversed hazard rate model</a>; <a href="/?q=ut%3Aempirical+cumulative+distribution+function">empirical cumulative distribution function</a>; <a href="/?q=ut%3Alogistic+map">logistic map</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 1519.94015" data-ciurl="/ci/07716609" data-biburl="/bibtex/07716609.bib" data-amsurl="/amsrefs/07716609.bib" data-xmlurl="/xml/07716609.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07716609.pdf" title="Zbl 1519.94015 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/10.1007/s11009-023-10035-0" aria-label="DOI for “Weighted fractional generalized cumulative past entropy and its properties”" title="10.1007/s11009-023-10035-0">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2106.10312"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abouammoh A, Abdulghani S, Qamber I (1994) On partial orderings and testing of new better than renewal used classes. 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