Algorithm for calculating the noncentral chi-square distribution

Abstract

This article presents a new algorithm for evaluating the noncentral chi-square distribution based on Parl's (1980) method of Neumann series expansion. It is applicable to both even and odd degrees of freedom, unlike most prior work, which has been directed at the even cases. Convergence tests and procedures for detection of loss of precision are given. The overall method is extremely simple to program, accurate to many decimal places where applicable, and efficient over a wide range of parameters. The method is reliable provided the proper expansion is chosen based on the parameters.