Abstract
Novel single-integral representations for the multivariate probability density functions and cumulative distribution functions of Gaussian class distributions (Rayleigh, Rician, Weibull, Nakagami- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> , 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -dimensional distribution.
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