{"title":"Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics","authors":"M. Akbari","doi":"10.1155/2020/4262574","DOIUrl":null,"url":null,"abstract":"In this paper, a new definition of the number of observations near the th order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions . Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":"2020 1","pages":"1-9"},"PeriodicalIF":1.3000,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4262574","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Probability and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2020/4262574","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, a new definition of the number of observations near the th order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions . Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.
在本文中，提出了一个新的定义，接近于一阶统计量的观测次数。然后根据质量概率函数、这些新的计数随机变量的一阶矩以及函数序列的完备性，建立了Pareto和一些相关分布的一些表征结果。最后，基于帕累托分布的这些新特征，提出了新的拟合优度检验。通过蒙特卡洛模拟，将所提出的测试的功率值与著名测试的功率值相比较，如Kolmogorov“Smirnov”和Cramer von Mises测试。
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