{"title":"A gamma tail statistic and its asymptotics","authors":"Toshiya Iwashita, B. Klar","doi":"10.1111/stan.12316","DOIUrl":null,"url":null,"abstract":"Asmussen and Lehtomaa [Distinguishing log‐concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function g which is able to distinguish between log‐convex and log‐concave tail behaviour of distributions, and proposed a randomized estimator for g. In this paper, we show that g can also be seen as a tool to detect gamma distributions or distributions with gamma tail. We construct a more efficient estimator ĝn based on U‐statistics, propose several estimators of the (asymptotic) variance of ĝn, and study their performance by simulations. Finally, the methods are applied to several data sets of daily precipitation.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"55 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistica Neerlandica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1111/stan.12316","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Asmussen and Lehtomaa [Distinguishing log‐concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function g which is able to distinguish between log‐convex and log‐concave tail behaviour of distributions, and proposed a randomized estimator for g. In this paper, we show that g can also be seen as a tool to detect gamma distributions or distributions with gamma tail. We construct a more efficient estimator ĝn based on U‐statistics, propose several estimators of the (asymptotic) variance of ĝn, and study their performance by simulations. Finally, the methods are applied to several data sets of daily precipitation.This article is protected by copyright. All rights reserved.
期刊介绍：
Statistica Neerlandica has been the journal of the Netherlands Society for Statistics and Operations Research since 1946. It covers all areas of statistics, from theoretical to applied, with a special emphasis on mathematical statistics, statistics for the behavioural sciences and biostatistics. This wide scope is reflected by the expertise of the journal’s editors representing these areas. The diverse editorial board is committed to a fast and fair reviewing process, and will judge submissions on quality, correctness, relevance and originality. Statistica Neerlandica encourages transparency and reproducibility, and offers online resources to make data, code, simulation results and other additional materials publicly available.
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