On the Cumulative Distribution Function of the Difference of Two Dependent Chi Square Random Variables

Abstract

In this article, we reexamine the derivation of the cumulative distribution function of the difference of two dependent chi-square random variables with the same degrees of freedom. We derive the cdf for this difference for even degrees of freedom and discuss a discrepancy that we have found with a reported cdf of this difference for even degrees of freedom in [6]. For odd degrees of freedom, an expression for the cdf seems to be unknown. In this case, we derive a representation of the cdf in terms of the Meijer G-function. These representations allowed us to compute percentiles for even and odd degrees of freedom.