  The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$)
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 of
the multivariate $\Gamma \Gamma$ distribution with arbitrary correlation.
Furthermore, we present novel approximating expressions for the PDF and CDF of
the sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Based
on this statistical analysis, we investigate the performance of radio frequency
and optical wireless communication systems. It is noteworthy that the presented
expressions include several previous results in the literature as special
cases.
