The k-μ-g random variable and the k-μ-g random process

In this paper, the k-μ-g random variable is considered. The k-μ-g random process arises from the κ-μ random process when the power of the k-μ random variable follows Gamma distribution. The closed form expressions for probability density function (PDF) and cumulative distribution function (CDF) of k-μ-g random variable are determined. Then, PDFs of the moment of n-th order of k-μ-g random variable, the ratio and product of two k-μ-g random variables are calculated in the closed form. Random variables are of crucial significance, not only for the statistical but also for the deterministic modeling of wireless mobile radio channels. The main contribution of using derived expressions is possibility to make easier performance analysis of wireless communication systems in the presence of k-μ-g short term fading, Gamma shadowing and k-μ-g cochannel interference.