The selection between Gumbel distributions and mixture models of Gumbel distribuions to analysis the data of maximum speed wind in Piracicaba, SP, Brazil

Renato Rodrigues SILVA[1]

Silvio Sandoval ZOOCHI1

§    ABSTRACT: Finite mixture models are normally used in situations where there is a suspect that a sample arises from two independents populations and where is not possible identify which of two populations belongs each elements of sample. However these models are also used in situations where a fit of a simple components these mixtures is unable describe the behavior studied phenomena because it allows for greater flexibility in modeling a heterogeneous population. Extreme value analysis using finite mixture models also have been studied by Thom (1967), Fahmi (1991), Walshaw (2000), Bortollo et al. (2005), Tartaglia et al. (2006). In this work, we fit the Gumbel distribution and Gumbel mixture to maximum speed wind of months april, may, august e september in Piracicaba, SP, because for these months, according to Silva e Zocchi (2005), the dataset of maximum speed wind are apparently bimodal. Futhermore, we choose the best model to data using tests of hypotheses and the  BIC selection criterium and we estimate occurrence probabilities of wind with speeds above 40 to 100 $km.h^{-1}$ and return levels with their respectives 95 \% confidence intervals. We conclude that the mixture models of Gumbel distribuions is the best model to analyze the maximum wind speed data for months of april e may and otherside the fit of Gumbel  distributions was the best fit to wind speed data for months of august e september.

§    KEYWORDS: Extreme value theory; return levels; mixture models.



[1] Departamento Ciências Exatas, Escola Superior de Agricultura ``Luiz de Queiroz", Universidade de São Paulo, Caixa Postal 9, CEP 13418-900 , Piracicaba, São Paulo, Brasil. E-mail: rrsilva@esalq.usp.br /  sszocchi@esalq.usp.br