On the convergence of the chi square and noncentral chi square distributions to the normal distribution


A simple and novel asymptotic bound for the maximum error resulting from the use of the central limit theorem to approximate the distribution of chi square and noncentral chi square random variables is derived. The bound enables the quick calculation of the number of degrees of freedom required to ensure a given approximation error, and is significantly tighter than bounds derived using the Berry-Esseen theorem. An application to widely-used approximations for the decision probabilities of energy detectors is also provided.

Free/open access

You can download the version of the paper that was accepted for publication here, or you can buy the published version here. The content of both versions is the same.

Source code

You can download a copy of the source code here.