Jailson Araujo Rodrigues

Sums, Products and Ratios for Crovelli’s Bivariate Gamma Distribution

Bivariate gamma distributions have been used successfully on modeling hydrological processes. In this work, supposing that X and Y follow the Crovelli’s bivariate gamma model, we deduce the exact distributions of the functions U = X + Y, P = XY and Q = X/(X + Y), as well as their respective moments. Those functions are important hidrological variables. A MAPLE code to compute the quantiles is provided. An application of the results is provided to rainfall data from Passo Fundo.

Combinações de variáveis aleatórias beta tipo II aplicadas em modelagem hidrológica

The distributions of products and ratios of random variables are used in various fields of applied science and they have been intensively studied by several researchers. In this work they are deducted the exact distributions of X Y , X /Y and X /(X +Y ) when X and Y are independent beta type II random variables. The results found are applied to real data analysis of rainfall occurred in cities in the state of Sergipe.