New Representations for the Multivariate Weibull Distribution with Constant Correlation

Abstract

Novel single integral representations for the multivariate probability density function (PDF) and cumulative distribution function (CDF) of Gaussian class Weibull distributions are derived. A special linear transformation of independent Gaussian random variables is used to generate correlated Weibull random variables. The solutions are expressed in terms of familiar functions which are available in common mathematical software. The well known equal (constant) correlation model is used in this paper. The advantage of the new representation is that only a single integral computation is needed to compute a L-dimensional distribution. Some applications of the new distribution representations are also given.