Approximating the sum of independent non-identical binomial random variables

Abstract

The distribution of the sum of independent non-identical binomial random variables is frequently encountered in areas such as genomics, healthcare, and operations research. Analytical solutions for the density and distribution are usually cumbersome to find and difficult to compute. Several methods have been developed to approximate the distribution, among which is the saddlepoint approximation. However, implementation of the saddlepoint approximation is non-trivial. In this paper, we implement the saddlepoint approximation in the sinib package and provide two examples to illustrate its usage. One example uses simulated data while the other uses real-world healthcare data. The sinib package addresses the gap between the theory and the implementation of approximating the sum of independent non-identical binomials.