Moments of Gamma type and three-parametric Mittag-Leffler function
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910667201576960 |
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| author | Wang, Min |
| author_facet | Wang, Min |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19330 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments of Gamma type and three-parametric Mittag-Leffler function Wang, Min Probability 33E12, 60E10, 60E07, 60E05 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. |
| title | Moments of Gamma type and three-parametric Mittag-Leffler function |
| topic | Probability 33E12, 60E10, 60E07, 60E05 |
| url | https://arxiv.org/abs/2410.19330 |