# New methods to compute the generalized chi-square distribution

arXiv: https://arxiv.org/abs/2404.05062 · HTML: https://mlsanity.com/paper/2404.05062/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 7 Apr 2024.

## Builds on (most cited first, 6 of 6)

- [Methods to integrate multinormals and compute classification measures](https://mlsanity.com/paper/2012.14331/) (2020)
- [Provable Probabilistic Safety and Feasibility-Assured Control for Autonomous Vehicles using Exponential Control Barrier Functions](https://mlsanity.com/paper/2205.03744/) (2022)
- [An efficient and accurate approximation to the distribution of quadratic forms of Gaussian variables](https://mlsanity.com/paper/2005.00905/) (2020)
- [Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations](https://mlsanity.com/paper/2203.03508/) (2022)
- [Purposeful Co-Design of OFDM Signals for Ranging and Communications](https://mlsanity.com/paper/2309.03076/) (2023)
- [Exact Consistency Tests for Gaussian Mixture Filters using Normalized Deviation Squared Statistics](https://mlsanity.com/paper/2312.17420/) (2023)

## Built on by (most cited first, 1 of 1)

- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)

## Abstract (arXiv)

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.