{"title":"Asymptotic approximations of expectations of power means","authors":"Tomislav Buri, Lenka Mihokovi","doi":"10.1111/stan.12331","DOIUrl":null,"url":null,"abstract":"Abstract In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general non‐negative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behaviour depending on sample size contributes to interesting connections with the power mean of probability distribution. 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":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/stan.12331","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
Abstract In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general non‐negative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behaviour depending on sample size contributes to interesting connections with the power mean of probability distribution. 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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