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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2507.06665 |
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| _version_ | 1866911047195033600 |
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| author | Sibisi, Nomvelo Karabo |
| author_facet | Sibisi, Nomvelo Karabo |
| contents | This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density. These two constructs, mixing and convolution, suffice to generate a rich family of distributions. An example is the positive Linnik distribution, which is known to arise from a product involving stable and gamma random variables. We show that gamma-Linnik convolution gives the Mittag-Leffler distribution and the Mittag-Leffler Markov chain associated with the growth of random trees. Building on that, we construct a new family of distributions with explicit densities. A particular choice of parameters for this family yields the Lamperti-type laws associated with occupation times for Markov processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributions based on Stable Mixtures and Gamma-Stable Convolutions Sibisi, Nomvelo Karabo Probability This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density. These two constructs, mixing and convolution, suffice to generate a rich family of distributions. An example is the positive Linnik distribution, which is known to arise from a product involving stable and gamma random variables. We show that gamma-Linnik convolution gives the Mittag-Leffler distribution and the Mittag-Leffler Markov chain associated with the growth of random trees. Building on that, we construct a new family of distributions with explicit densities. A particular choice of parameters for this family yields the Lamperti-type laws associated with occupation times for Markov processes. |
| title | Distributions based on Stable Mixtures and Gamma-Stable Convolutions |
| topic | Probability |
| url | https://arxiv.org/abs/2507.06665 |