On Approximating a Generalized Binomial by Binomial and Poisson Distributions

Abstract

The aim of this paper is to approximate a generalized binomial distribution by binomial and Poisson distributions. Using the ω-function and the two Stein identities, the main result of each approximation in terms of the total variation distance between two distributions and its upper bound is obtained. Moreover, some numerical examples have been given to show applications of the results concerning the three special cases of generalized binomial distribution (binomial, hypergeometric and Pólya distributions).