  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.
