A unified semi-analytical technique to evaluate the distributions of products of non-identically distributed Weibull random variables

In this paper we derived the probability density function of the product of independent non-identically distributed Weibull RVs. The derivation is based on the use of the Mellin transformation along with the Residue theorem to evaluate the attained complex integral. The resultant integrands have only elementary functions, such as exponentials and algebraic power functions and can, therefore, be explicitly evaluated to any degree of accuracy using any symbolic mathematics based software. The distribution of the product of independent and identically distributed (i.i.d) Weibull RVs are also evaluated. The proposed method avoids the computational burden of residuals of a product of functions. Hence our results are expected to be of significant practical use to evaluate the error rate performance of any Mary orthogonal faded systems in indoor and outdoor wireless environments.