什么时候离散威布尔分布是无限可分的？

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-08-10 DOI:10.1016/j.spl.2024.110238

Markus Kreer , Ayse Kizilersu , Anthony W. Thomas

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引用次数: 0

摘要

对于离散 Weibull 概率分布，我们证明只有当形状参数位于 0<β≤1 范围内时，它才是无限可分的。证明基于 Steutel 和 van Harn (2004) 的一些结果。在这种情况下，我们将构建相应的复合泊松分布，从而构建相关的莱维过程。

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When is the discrete Weibull distribution infinitely divisible?

For the discrete Weibull probability distribution we prove that it is only infinitely divisible if the shape parameter lies in the range $0 < β \leq 1$ . 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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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.