New methods to compute the generalized chi-square distribution
This provides incremental improvements in computational statistics for researchers analyzing multivariate normal distributions.
The authors developed four new mathematical methods (two exact, two approximate) with accompanying software to compute the cumulative distribution function, probability density function, and inverse cumulative distribution function of the generalized chi-square distribution, enabling accurate measurement of large discriminability index values between multivariate normal distributions.
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.