Propriedades das distribuições bivariadas de crovelli, gumbel tipo I e gama beta tipo II, com uma aplicação a dados de precipitação pluviométrica

Abstract

One can find a lot of bivariate probability distributions when studying the pooled behavior of two random variables, as well as their sum, product or difference. In particular, such approach had been extensively used in hydrology, where the target variables are the run period and the inter consecutive runs period. In this work we deduce properties for the Crovelli bivariate gamma model and the Gumbel Type I bivariate exponential model, as well as their sum, product and difference. Those properties are not described in specialized literature. We also introduce a new bivariate distribution, which we called gamma beta II. As an application, we fitted these three distributions to rain precipitation data. The results show acceptable behavior of those models