Special functions are used in almost all areas of statistics. Statistical densities are basically elementary special functions or product of such functions. Hence, the theory of special functions is directly applicable to statistical distribution theory. While studying generalized densities, structural properties of densities, Bayesian inference, distributions of test statistics, characterization of densities and related studies of probability theory, stochastic processes and time series problems, and special functions and generalized special functions in the categories of Meijer’s G-functions and H-functions come in naturally.