When is the discrete Weibull distribution infinitely divisible?

被引：0

作者：

Kreer, Markus ^{[1
]}

Kizilersu, Ayse ^{[2
]}

Thomas, Anthony W. ^{[3
]}

机构：

[1] Feldbergschule, Oberhochstadter Str 20, D-61440 Oberursel, Germany

[2] Adelaide Univ, Special Res Ctr Subatom Struct Matter CSSM, Sch Phys Sci, Dept Phys, Adelaide, SA 5005, Australia

[3] Adelaide Univ, Dept Phys, CSSM, Adelaide, SA 5005, Australia

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 215卷

关键词：

Discrete Weibull distribution; Infinite divisibility; Log-convexity; Compound distribution; L & eacute; vy process;

D O I：

10.1016/j.spl.2024.110238

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For the discrete Weibull probability distribution we prove that it is only infinitely divisible if the shape parameter lies in the range 0 < beta <= 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 Levy process.

引用

页数：5

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