Accurate Approximation to the PDF of the Product of Independent Rayleigh Random Variables

A novel approximation to the probability density function for the product of arbitrary n independent Rayleigh random variables is proposed. The approximation is based on a transformed Nakagami-m distribution. Unlike the existing exact density function in the literature, the new approximation is compact and only employs simple functions that are very easy to calculate and to manipulate. New maximum likelihood estimators for the distribution parameters are also derived that are otherwise impossible using the existing exact density function. A new estimator using the logarithm of the sample and a new estimator without knowledge of the number of variables are also developed. Numerical results show that the new approximation has very high accuracy in most cases considered. Numerical results also show that the new estimators using maximum likelihood and sample logarithm outperform the existing estimators.