Characterizations of probability distributions based on discrete p-monotonicity

Abstract

In this paper, a general characterization of a class of discrete self-decomposable distributions based on discrete p-monotonicity is obtained. This result can be thought as the discrete version of an earlier result due to Shanbhag (1972), Artikis (1982) and Alamatsaz (1985). Applying this result, discrete versions of some recent characterizations obtained by Kotz and Steutel (1988), Huang and Chen (1989) and Alamatsaz (1993) are given. Also, as a by-product of another related result, an extension of Forst's (1979) characterization of discrete self-decomposable Poisson mixtures is arrived at. © 1995.