Approximating the Sum of Independent Non-Identical Binomial Random Variables

TL;DR

This paper introduces the sinib R package that implements saddlepoint approximation for efficiently estimating the distribution of sums of independent non-identical binomial variables, a common problem in various fields.

Contribution

The paper develops and provides an R package for saddlepoint approximation, making it easier to compute distributions of sums of non-identical binomials in practice.

Findings

The sinib package successfully implements saddlepoint approximation.

Demonstrations include simulated and real healthcare data.

The package bridges the gap between theory and practical application.

Abstract

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