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

Min Wang

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arXiv · 2410.19330

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

Min Wang

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Abstract

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.

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Min Wang. 2024-10-25. Moments of Gamma type and three-parametric Mittag-Leffler function. https://arxiv.org/abs/2410.19330

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