Intensity-duration models based on bivariate gamma distributions

Abstract

Bivariate and univariate gamma distributions are some of the most popular models for hydrological processes. In fact, the intensity and the duration of most hydrological variables are frequently modeled by gamma distributions. This raises the important question: what is the distribution of the total amount = intensity $\times$ duration? In this paper, the exact distribution of $P = X Y$ and the corresponding moment properties are derived when the random vector $(X, Y)$ has two of the most flexible bivariate gamma distributions. The expressions turn out to involve several special functions.