Quasi-geometric infinite divisibility

Abstract

The object of this paper is to introduce and study the concept of quasi-geometric infinite divisibility for distributions on ${\mathbf{R}}_{+}$. These distributions arise as mixing distributions of (discrete) geometric infinitely divisible Poisson mixtures. Several characterizations and closure properties are presented. A connection between quasi-geometric infinite divisibility and log-convex (log-concave) distributions is established. A generalized notion of quasi-infinite divisibility is also discussed.