Moments of Gamma type and three-parametric Mittag-Leffler function

Autor:	Wang, Min
Rok vydání:	2024
Předmět:	Mathematics - Probability 33E12 60E10 60E07 60E05
Druh dokumentu:	Working Paper
Popis:	We study a class of positive random variables having moments of Gamma type, whose density can be expressed by the three-parametric Mittag-Leffler functions. We give some necessary conditions and some sufficient conditions for their existence. As a corollary, we give some conditions for non-negativity of the three-parametric Mittag-Leffler functions. As an application, we study the infinite divisibility of the powers of half $\a$-Cauchy variable. In addition, we find that a random variable $\X$ having moment of Gamma type if and only if $\log \X$ is quasi infinitely divisible. From this perspective, we can solve many Hausdorff moment problems of sequences of factorial ratios. Comment: 12 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.19330 Zobrazit plný text záznamu View this record from Arxiv