Distribuição de valores extremos generalizada inflada de zeros

Abstract

Extreme events are usually responsible for producing big gains or big losses to society. There is already a specific distribution, known as Generalized Extreme Values Distribution (GEV), developed to predict and prevent such events. However, in many situations with extreme data, there are the presence of excessive zeros in the database, making analysis difficult and difficult to estimate. Influenced Zero Distribution (ZID) is recommended to model such data that has inflated zeros. It is the objective of this work to create a new distribution to model data of extreme and inflated values of zeros. Therefore, a mixture of the GEV and ZID distributions was made, as well as a Bayesian approach, in order to obtain a better fit in applications with data of inflated maximums of zeros. The daily precipitation of rainfall in the city of Natal in the state of Rio Grande do Norte and in the cities of Paulistana, Picos, S˜ao Jo˜ao do Piau´ı and Teresina in the state of Piau´ı were chosen for analysis. It was also used the standard GEV distribution to model the same data collected by way of comparison, and thus, through measurements and estimates made by the two distributions, to verify the quality of the adjustment found by the new distribution of Extremes Inflated Zeros Values (IGEV). Therefore, it was verified that the model was well developed, being able to estimate well the maximum data, even an excessive amount of zeros, and the standard GEV could not find the equilibrium distribution when the data given have many zeros. In addition, when the data of extreme values does not have inflated zeros, the new model converges to the standard GEV, identifying the absence of zeros.