Quasi-infinite divisibility of a class of distributions with discrete part

Abstract

We consider distributions on R \mathbb {R} that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its characteristic function is bounded away from zero, thus giving a new class of quasi-infinitely divisible distributions. Moreover, for this class of distributions we characterize the existence of the g g -moment for certain functions g g .