Convolutions and Mixtures of Gamma, Stable and Mittag-Leffler Distributions

Nomvelo Karabo Sibisi

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arXiv · 2402.15228

Convolutions and Mixtures of Gamma, Stable and Mittag-Leffler Distributions

Nomvelo Karabo Sibisi

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Abstract

This paper uses convolutions of the gamma density and the one-sided stable density to construct higher level densities. The approach is applied to constructing a 4-parameter Mittag-Leffler density, whose Laplace transform is a corresponding Mittag-Leffler function, which is completely monotone (CM) by construction. Laplace transforms of mixtures of the stable densities with respect to the 4-parameter Mittag-Leffler distribution are compositions of the Mittag-Leffler functions with Bernstein functions, thereby generating a rich family of CM variants of the base CM Mittag-Leffler functions, including known instances as special cases.

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Nomvelo Karabo Sibisi. 2024-02-23. Convolutions and Mixtures of Gamma, Stable and Mittag-Leffler Distributions. https://arxiv.org/abs/2402.15228

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