Momentos-L na estimação dos parâmetros da distribuição generalizada de valores extremos

Abstract

The Extreme Value Theory (EVT) ​​is an important tool used in the analysis of extreme events. The analysis of such events allows for better planning in human actions in order to minimize the effects caused by them. A distribution from EVT that is widely used in extreme events modeling is the generalized extreme value distribution (GEV). Several estimation methods can be used to estimate the GEV distribution parameters. Among the most widely used estimators are the maximum likelihood estimators. However, these estimators are not suitable, or do not exist, when the shape parameter of the GEV distribution is less than -0.5. In these situations it is necessary to use another estimator. In this sense, the objective of this work was to evaluate the adequacy of the use of the L-moment estimators in the adjustment of the GEV distribution, comparing the precision and accuracy of these estimators with the precision and accuracy of the maximum likelihood estimators and to use these two estimators to adjust the GEV distribution to a set of real data that contains the estimate of the parameter form between -1 and - 0.5. It was found that for negative values ​​of the shape parameter of the GEV the L-moment method is indicated for sample sizes less than or equal to 25, with the shape parameter with values ​​close to zero the L-moments is indicated for sample sizes less than or equal to 35 and for positive values ​​of the form parameter the L-moments should be used in all sample sizes.