Estimation of extreme percentiles in Birnbaum-Saunders distributions

Authors:
Filidor Vilca;Lucia Santana;Víctor Leiva;N. Balakrishnan
Affiliations:
Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil;Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil;Departamento de Estadística, CIMFAV, Universidad de Valparaíso, Valparaíso, Chile and Departamento de Matemáticas, Universidad de Antofagasta, Antofagasta, Chile;Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

The Birnbaum-Saunders distribution has recently received considerable attention in the statistical literature, including some applications in the environmental sciences. Several authors have generalized this distribution, but these generalizations are still inadequate for predicting extreme percentiles. In this paper, we consider a variation of the Birnbaum-Saunders distribution, which enables the prediction of extreme percentiles as well as the implementation of the EM algorithm for maximum likelihood estimation of the distribution parameters. This implementation has some advantages over the direct maximization of the likelihood function. Finally, we present results of a simulation study along with an application to a real environmental data set.