Improved statistical inference for the two-parameter Birnbaum-Saunders distribution

Authors:
Artur J. Lemonte;Francisco Cribari-Neto;Klaus L. P. Vasconcellos
Affiliations:
Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife/PE 50740-540, Brazil;Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife/PE 50740-540, Brazil;Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife/PE 50740-540, Brazil
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

We develop nearly unbiased estimators for the two-parameter Birnbaum-Saunders distribution [Birnbaum, Z.W., Saunders, S.C., 1969a. A new family of life distributions. J. Appl. Probab. 6, 319-327], which is commonly used in reliability studies. We derive modified maximum likelihood estimators that are bias-free to second order. We also consider bootstrap-based bias correction. The numerical evidence we present favors three bias-adjusted estimators. Different interval estimation strategies are evaluated. Additionally, we derive a Bartlett correction that improves the finite-sample performance of the likelihood ratio test in finite samples.