On the Multivariate Gamma–Gamma Distribution With Arbitrary Correlation and Applications in Wireless Communications
Jiayi Zhang, Michail Matthaiou, George K. Karagiannidis, Linglong Dai · IEEE Transactions on Vehicular Technology · 2015
The statistical properties of the multivariate gamma-gamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (pdf), cumulative distribution function (cdf), and moment generation function (mgf) of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the pdf and cdf of the sum of ΓΓ random variables (RVs) with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency (RF) and optical wireless communication systems. It is worth noting that the presented expressions include several previous results in the literature as special cases.