A FAMILY OF DISCRETE-DISTRIBUTIONS

Ambagaspitiya and Balakrishnan (1994a) used the identity ]GRAPHICS[ with p0(a, b) = exp(- a) to obtain a recursive formula for computing the distribution function of the compound generalized Poisson distribution. In this paper, we consider the discrete distribution family with the property ]GRAPHICS[ which is a generalization of the first identity. We prove that weighted generalized Poisson distributions and weighted generalized negative binomial distributions with weights of the form w(a + bn; b) are two subclasses in the family. We provide a recursive formula for computation of respective compound distributions. Also we discuss the stability of the recursion as well as handling overflow/underflow problems.