The Product and the Ratio of α - μ Random Variables and Outage, Delay-Limited and Ergodic Capacities Analysis

Historically, the algebra of random variables has been a discipline of interest to statisticians. On the other hand, in the last ve decades special functions and numerical tools have become largely available, implying other scientists to apply results regarding this area of knowledge. In special, while studying the capacity of wireless networks, electrical and network engineers rely on evaluating the probability density function of the ratio of random variables. In the present paper, the probability distribution function of α-μ random variables is derived in terms of the H-function and used to evaluate the outage, delay-limited and ergodic capacities, generalizing earlier results in the literature. The results are evaluated by means of an original Mathematica routine and shown to be in accordance with established theoretical results.