Paper ID: 2404.05062

New methods to compute the generalized chi-square distribution

Abhranil Das

We present several new mathematical methods (ray-trace, inverse Fourier transform and ellipse) and 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 multinormals. We characterize the performance and limitations of these and previous methods, and recommend the best methods to use for each part of each type of distribution. We also demonstrate the speed and accuracy of our new methods against previous methods across a wide sample of distributions.

Submitted: Apr 7, 2024