Document Zbl 07979569

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Stat., Theory Methods</a> <a href="/?q=in%3A523433" title="Articles in this Issue">54, No. 1, 84-97 (2025)</a>. </div> <div class="abstract">Summary: Rényi entropy has been widely used in many applications. However, the significance of the parameter $\alpha$ in Rényi entropy and how to determine the value of $\alpha$ is still an open issue. To explore the significance of $\alpha$, a scaled Rényi entropy is proposed in this article, where $\alpha$ is a scaled constant. Based on the information dimension of mass function in a power set whose uncertainty is measured by Deng entropy, the scale of $\alpha$ in Rényi entropy of the probability distribution is determined. One numerical example is given to show its properties. The scaled Rényi entropy and Rényi entropy are then applied to the C 4.5 decision tree and active learning to compare the usefulness of scaled Rényi and Rényi entropy.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-XX" title="MSC2020">62-XX</a> </td> <td class="space"> Statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AR%C3%A9nyi+entropy">Rényi entropy</a>; <a href="/?q=ut%3Ascaled+R%C3%A9nyi+entropy">scaled Rényi entropy</a>; <a href="/?q=ut%3Adeng+entropy">deng entropy</a>; <a href="/?q=ut%3Ainformation+dimension">information dimension</a>; <a href="/?q=ut%3Adecision+tree">decision tree</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 07979569" data-ciurl="/ci/07979569" data-biburl="/bibtex/07979569.bib" data-amsurl="/amsrefs/07979569.bib" data-xmlurl="/xml/07979569.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07979569.pdf" title="Zbl 07979569 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/10.1080/03610926.2024.2301986" aria-label="DOI for “On the scaled Rényi entropy and application”" title="10.1080/03610926.2024.2301986">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">Babajanyan, S., Allahverdyan, A., and Cheong, K. 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