Nomvelo Karabo Sibisi
Published 2024-02-23, updated 2024-04-15Version 5
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.
Convolutions of long-tailed and subexponential distributions
A note on mixture representations for the Linnik and Mittag-Leffler distributions and their applications
On the dual representations of Laplace transforms of Markov processes
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