{"title":"Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions","authors":"","doi":"10.1007/s00184-024-00947-3","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Stimulated by the need of describing useful notions related to information measures, we introduce the ‘pdf-related distributions’. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Metrika","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00184-024-00947-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Stimulated by the need of describing useful notions related to information measures, we introduce the ‘pdf-related distributions’. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy.
摘要 由于需要描述与信息度量相关的有用概念，我们引入了 "pdf 相关分布"。这些分布是通过绝对连续随机变量自身的概率密度函数进行变换而定义的。我们将参考分布的一般形式、量值以及可靠性理论的一些相关概念，研究它们的主要特征。这使我们能够获得与 pdf 有关的分布的特征，即指数型和拉普拉斯型分布也是均匀的。我们还通过使用合适的随机阶次，解决了对 pdf 相关分布进行随机比较的问题。最后，我们利用给出的结果分析了一些有用的信息度量的性质并进行了比较，如微分熵和熵。
期刊介绍：
Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
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