An analytical derivation of the storm volume distribution is given. The single storm is modeled as a rectangular pulse having non-independent random duration and intensity. The structure of the dependence between storm duration and intensity is given via a suitable 2-Copula, and the marginal distributions are endowed with Generalized Pareto laws, as recently pointed out in the hydrological Literature. The statistical properties of the rainfall volume are investigated, both analytically and using simulated samples; an application to rainfall data is also shown.