New generalised approximation methods for the cumulative distribution function of arbitrary multivariate Rayleigh random variables

Abstract

Based on our previous works, we revise a simple series expansion for multivariate probability density functions (PDF) of the Rayleigh distribution. From there we derive a similar expression for the cumulative density function (CDF) of multivariate Rayleigh random variables of arbitrary dimension and covariance matrix. The CDF is of particular interest as it can be used to compute outage probabilities of multi-channel wireless systems, for which we provide an example. We compare the performance of the newly proposed approximation to recently proposed methods based on numerical integration methods.