Distribuições bivariadas Gama, Exponencial e a distribuição Beta Tipo II univariada aplicadas a dados de precipitação pluviométrica

Abstract

The rainfalls are recurrent phenomena with random uncertain occurrence and intensity resulting from the condensed water in the atmosphere that reaches the earth’s surface by gravity. The intensity and frequency that this phenomenon occurs, direct influence on the natural habitats, ecosystems and many economic and social sectors from agriculture, transport, urban water supply. In this work, we present some properties of bivariate gamma distributions for Smith, Adelfang and Tubbs’s bivariate gamma distributions, Gumbel´s type I bivariate exponential and univariate beta type I distribution. These models are used in the analysis of important variables, period rainfall and the contiguous period without rainfall. The results indicate the adequacy of the three models. Using the Gumbel-Barnett co- pula was built a bivariate exponential distribution which generalizes the Gumbel´s type I bivariate exponential. The main properties of this distribution were derived. The model was used to analyze the structure between the sequences of days with rainfall and sequences of days without rainfall. The results indicate that the model is viable.