The distribution of the product of independent Rayleigh random variables

We derive the exact probability density functions (pdf) and distribution functions (cdf) of a product of n independent Rayleigh distributed random variables. The case n = 1 is the classical Rayleigh distribution, while n >= 2 is the n-Rayleigh distribution that has recently attracted interest in wireless propagation research. The distribution functions are derived by using an inverse Mellin transform technique from statistics, and are given in terms of a special function of mathematical physics, the Meijer G-function. Series forms of the distribution function are also provided for n = 3, 4, 5. We also derive a computationally simple moment-based estimator for the parameter occurring in the distribution, and evaluate its variance.