New methods to compute the generalized chi-square distribution

TL;DR

This paper introduces four novel mathematical methods, including two exact and two approximate techniques, for computing the generalized chi-square distribution's functions, with open-source software, enhancing speed and accuracy for statistical analysis.

Contribution

The paper presents new methods for computing the generalized chi-square distribution, offering improved speed and tail accuracy, along with open-source implementations.

Findings

Methods outperform previous approaches in speed and accuracy.

Some methods excel in tail probability estimation.

Open-source software facilitates practical application.

Abstract

We present four new mathematical methods, two exact and two approximate, along with open-source software, to compute the cdf, pdf and inverse cdf of the generalized chi-square distribution. Some methods are geared for speed, while others are designed to be accurate far into the tails, using which we can also measure large values of the discriminability index $d'$ between multivariate normal distributions. We compare the accuracy and speed of these and previous methods, characterize their advantages and limitations, and identify the best methods to use in different cases.