Saddlepoint approximations for the sum of independent non-identically distributed binomial random variables

Abstract

We discuss saddlepoint approximations to the distribution of the sum of independent non-identically distributed binomial random variables. We examine the accuracy of the saddlepoint methods for a sum of 10 binomials with different sets of parameter values. The numerical results indicate that the saddlepoint approximations provide very accurate estimates for the probability mass function and the right-tail probabilities for the cumulative distribution function of the sum.