Novel Simple Representations for Gaussian Class Multivariate Distributions With Generalized Correlation

Novel single-integral representations for the multivariate probability density functions and cumulative distribution functions of Gaussian class distributions (Rayleigh, Rician, Weibull, Nakagami- m, and generalized Rician) are derived. The solutions are expressed in terms of well-known functions which are available in common mathematical software. The marginal random variables are not necessarily identically distributed as is the case for some past solutions. A generalized correlation structure based on a special linear transformation of independent Gaussian random variables is used in this study. The advantage of the new representation is that only a single-integral computation is needed to compute an N-dimensional distribution.