{"title":"A comment on rates of convergence for density function in extreme value theory and Rényi entropy","authors":"Ali Saeb","doi":"10.1090/tpms/1191","DOIUrl":null,"url":null,"abstract":"De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order \n\n \n β\n \\beta\n \n\n (\n\n \n \n β\n >\n 1\n \n \\beta >1\n \n\n) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order \n\n \n β\n \\beta\n \n\n of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1191","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order
β
\beta
(
β
>
1
\beta >1
) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order
β
\beta
of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.
De Haan和Resnick[Ann.Probab.10（1982），no.2396–413]已经表明，具有连续可微密度的独立同分布（iid）随机变量的归一化样本极大值的β\β阶Rényi熵（β>1\β>1）收敛于极大稳定律的β\贝塔阶Rény熵。本文讨论了极值理论中密度函数的收敛速度。最后，我们研究了Rényi熵在归一化样本最大值情况下的收敛速度。
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
