Product of $\alpha$– $\mu$ Variates

Exact closed-form expressions for the probability density function and the cumulative distribution function for the product of an arbitrary number of independent non-identically distributed α-μ variates are derived. The expressions are given in terms of the Meijer G-function, and in terms of afinite sum of hypergeometric functions, and can be easily computed by means of well-known mathematical software tools. As a consequence of the generality of the α-μ distribution as well as of the results, these statistics comprise those for the product of arbitrary combinations of other useful distributions such as One-Sided Gaussian, Negative Exponential, Rayleigh, Weibull, Gamma, and Nakagami-m. As an application example, the outage probability for the cascade channel is presented.