{"title":"Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter","authors":"Volodymyr Braiman, Anatoliy Malyarenko, Yuliya Mishura, Yevheniia Anastasiia Rudyk","doi":"arxiv-2403.08805","DOIUrl":null,"url":null,"abstract":"We consider two types of entropy, namely, Shannon and R\\'{e}nyi entropies of\nthe Poisson distribution, and establish their properties as the functions of\nintensity parameter. More precisely, we prove that both entropies increase with\nintensity. While for Shannon entropy the proof is comparatively simple, for\nR\\'{e}nyi entropy, which depends on additional parameter $\\alpha>0$, we can\ncharacterize it as nontrivial. The proof is based on application of Karamata's\ninequality to the terms of Poisson distribution.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.08805","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider two types of entropy, namely, Shannon and R\'{e}nyi entropies of
the Poisson distribution, and establish their properties as the functions of
intensity parameter. More precisely, we prove that both entropies increase with
intensity. While for Shannon entropy the proof is comparatively simple, for
R\'{e}nyi entropy, which depends on additional parameter $\alpha>0$, we can
characterize it as nontrivial. The proof is based on application of Karamata's
inequality to the terms of Poisson distribution.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
