Approximation to Distribution of Product of Random Variables Using   Orthogonal Polynomials for Lognormal Density
  We derive a closed-form expression for the orthogonal polynomials associated with the general lognormal density. The result can be utilized to construct easily computable approximations for probability density function of a product of random variables, when the considered variates are either independent or correlated. As an example, we have calculated the approximative distribution for the product of Nakagami-m variables. Simulations indicate that accuracy of the proposed approximation is good with small cross-correlations under light fading condition. 
Zhong Zheng, Lu Wei, Jyri H\"am\"al\"ainen, Olav Tirkkonen
cs.IT math.IT