{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1111/stan.12316","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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