On the number of successes in dependent trials

Abstract

A new approach to the study of the distributions of sums of n Bernoulli variables by conditional distributions is considered. This leads to a characterization of binomial distribution, and provides a simple approach to the study of generalized binomial distributions. We show that the binomial distribution and Poisson's binomial distribution can be derived as the distribution of sum of dependent Bernoulli random variables. Finally the problem of Poisson approximation to the generalized binomial distribution is investigated.