Estimation of extreme percentiles in Birnbaum–Saunders distributions

• Published in: Computational statistics & data analysis Vol. 55; no. 4; pp. 1665 - 1678
• Main Authors: Vilca, Filidor, Santana, Lucia, Leiva, Víctor, Balakrishnan, N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-04-2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Algorithms; Computation; Computer simulation; Data processing; Distribution theory; EM and ECM algorithms; EM and ECM algorithms Monte Carlo simulations Skew distributions; Exact sciences and technology; General topics; Mathematical analysis; Mathematical models; Mathematics; Maximization; Maximum likelihood estimation; Monte Carlo simulations; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Skew distributions; Statistics; Skew distributions; EM and ECM algorithms; Monte Carlo simulations; Percentile; Statistical distribution; Generalized function; Prediction theory; Stochastic method; Stochastic process; Statistical simulation; Implementation; Hypothesis test; Statistical test; Distribution function; Function maximization; Approximation theory; Likelihood function; Monte Carlo method; Data analysis; Prediction; Statistical estimation; Statistical method; Numerical analysis; Statistical computation; Skewness measure; Environment; Filtering theory; Maximum likelihood; EM algorithm
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.10.023

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.