{"title":"Discrete Pareto Distributions","authors":"Amrutha Buddana, T. Kozubowski","doi":"10.1515/eqc-2014-0014","DOIUrl":null,"url":null,"abstract":"Abstract We review several common discretization schemes and study a particular class of power-tail probability distributions on integers, obtained by discretizing continuous Pareto II (Lomax) distribution through one of them. Our results include expressions for the density and cumulative distribution functions, probability generating function, moments and related parameters, stability and divisibility properties, stochastic representations, and limiting distributions of random sums with discrete-Pareto number of terms. We also briefly discuss issues of simulation and estimation and extensions to multivariate setting.","PeriodicalId":360039,"journal":{"name":"Economic Quality Control","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"31","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economic Quality Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/eqc-2014-0014","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 31
Abstract
Abstract We review several common discretization schemes and study a particular class of power-tail probability distributions on integers, obtained by discretizing continuous Pareto II (Lomax) distribution through one of them. Our results include expressions for the density and cumulative distribution functions, probability generating function, moments and related parameters, stability and divisibility properties, stochastic representations, and limiting distributions of random sums with discrete-Pareto number of terms. We also briefly discuss issues of simulation and estimation and extensions to multivariate setting.
摘要回顾了几种常用的离散化方案，研究了一类特殊的整数上的幂尾概率分布，该概率分布是通过其中一种离散化连续Pareto II (Lomax)分布得到的。我们的研究结果包括密度和累积分布函数的表达式，概率生成函数，矩和相关参数，稳定性和可除性，随机表示，以及具有离散pareto数项的随机和的极限分布。我们还简要地讨论了模拟和估计的问题以及对多元设置的扩展。
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