{"title":"When is the discrete Weibull distribution infinitely divisible?","authors":"Markus Kreer , Ayse Kizilersu , Anthony W. Thomas","doi":"10.1016/j.spl.2024.110238","DOIUrl":null,"url":null,"abstract":"<div><p>For the discrete Weibull probability distribution we prove that it is only infinitely divisible if the shape parameter lies in the range <span><math><mrow><mn>0</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>1</mn></mrow></math></span> . The proof is based on some results of Steutel and van Harn (2004). For this case we construct the corresponding compound Poisson distribution and thus the related Lévy process.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224002074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For the discrete Weibull probability distribution we prove that it is only infinitely divisible if the shape parameter lies in the range . The proof is based on some results of Steutel and van Harn (2004). For this case we construct the corresponding compound Poisson distribution and thus the related Lévy process.
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