Approximating the Mode of the Non-Central Chi-Squared Distribution

Abstract

In this paper we consider the probability density function (pdf) of the non-central χ2 distribution with arbitrary number of degrees of freedom and non-centrality. For this function we find the approximate location of the maximum and discuss related edge cases of 1 and 2 degrees of freedom. We also use this expression to demonstrate the improved performance of the C++ Boost’s implementation of the non-central χ2 and extend the domain of its applicability.