Mixture representation of Linnik distribution revisited

Abstract

Let Y[alpha] have a Linnik distribution, given by the characteristic function [psi](t) = (1 + t [alpha])-1. We extend the result of Kotz and Ostrovskii (1996) and show that Y[alpha] admits two different representations, where 0Geometric stable law Heavy tailed distribution Mittag-Leffler distribution Mixture Random summation Simulation Stable law