{"title":"Dirac distributions related to sums of independent nonidentically uniform random variables","authors":"Youssef Lazar, Bander N. Almutairi","doi":"10.1214/20-BJPS484","DOIUrl":null,"url":null,"abstract":"The aim of this note is to give an elegant proof of a result due to E. G. Olds which concerns the density distribution of the sum of independent uniform random variables non-identically distributed. The proof uses both analytical and combinatorial properties of Dirac distributions and their convolutions. The method is new and can apply to other situations.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/20-BJPS484","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this note is to give an elegant proof of a result due to E. G. Olds which concerns the density distribution of the sum of independent uniform random variables non-identically distributed. The proof uses both analytical and combinatorial properties of Dirac distributions and their convolutions. The method is new and can apply to other situations.
期刊介绍：
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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