A new multivariate gamma distribution and its fitting to empirical streamflow data

Abstract

A new multivariate gamma distribution is presented which can successfully be fitted to empirical data where the one‐dimensional marginal distributions are gamma distributions with prescribed parameters and the correlations are nonnegative. It is not intended to give explicit formulae either for the joint density or for the joint characteristic function of the random variables. Our representation of the individual gamma‐distributed random variables will be used for simulation, with the aid of which we approximate probabilities of sets in higher‐dimensional spaces. Since streamflow and other hydrological data frequently follow gamma distribution and also they are frequently stochastically dependent, our multivariate distribution and fitting technique seems to be of particular interest from the hydrological point of view.