New mixture representations of the generalized Mittag-Leffler distribution and their applications

The article provides new mixture represenations for the generalized Mittag-Leffler distribution. In particular, it is shown that for values of the “generalizing” parameter not exceeding one, the generalized Mittag-Leffler distribution is a scale mixture of the half-normal distribution laws, classic Mittag-Leffler distributions, or generalized Mittag-Leffler distributions with the larger values of the characteristic index. The explicit expressions for mixing quantities are given for all cases. The obtained representations allow proposing new algorithms for modeling random variables with the generalized Mittag-Leffler distribution and formulating new limit theorems in which such distributions appear as the limit ones.