The Product and the Ratio of α - μ Random Variables and Outage, Delay-Limited and Ergodic Capacities Analysis
Issue: 2014 - Volume 4 [Issue 1]
Pushpa N. Rathie *
Department of Statistics, University of Brasilia, Campus Universitrio Darcy Ribeiro, Brasilia, DF, 70910-900, Brazil
Arjun K. Rathie
Department of Mathematics, School of Mathematical and Physical Sciences, Central University of Kerala, Riverside Transit Campus, Padennakkad P.O. Nileshwar, Kasaragod - 671 328, Kerala, India
Luan C. de S. M. Ozelim
Department of Civil and Environmental Engineering, University of Brasilia, Campus Universitrio Darcy Ribeiro, Brasilia, DF, 70910-900, Brazil
*Author to whom correspondence should be addressed.
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.
Keywords: α-μ random variables, Mellin transform, outage capacity, delay-limited capacity, ergodic capacity