Quasi-geometric infinite divisibility

TL;DR

This paper introduces and explores quasi-geometric infinite divisibility for distributions on positive real numbers, linking it to geometric infinitely divisible Poisson mixtures and properties like log-convexity.

Contribution

It defines the concept of quasi-geometric infinite divisibility, provides characterizations, closure properties, and connects it to log-convex and log-concave distributions.

Findings

Characterization of quasi-geometric infinite divisibility

Closure properties under certain operations

Connection to log-convex and log-concave distributions

Abstract

The object of this paper is to introduce and study the concept of quasi-geometric infinite divisibility for distributions on $\bf R_+$. 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.