Lifetime analysis based on the generalized Birnbaum-Saunders distribution

Authors:
Víctor Leiva;Marco Riquelme;N. Balakrishnan;Antonio Sanhueza
Affiliations:
Departamento de Estadística, CIMFAV, Universidad de Valparaíso, Casilla de correos 5030, Valparaíso, Chile;Instituto de Ciencias Básicas, Universidad Católica del Maule, Talca, Chile;Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada;Departamento de Matemática y Estadística, Universidad de La Frontera, Temuco, Chile
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

In this paper, we consider a family of generalized Birnbaum-Saunders distributions and present a lifetime analysis based mainly on the hazard function of this model. In addition, we carry out maximum likelihood estimation by using an iterative algorithm, which produces robust estimates. Asymptotic inference is also presented. Next, the quality of the estimation method is examined by means of Monte Carlo simulations. We then provide a practical example to illustrate the obtained results. From this example and based on goodness-of-fit methods, we show that the GBS distribution results in a more appropriate model for modeling fatigue data than other models commonly used to model this type of data. Finally, we estimate the hazard function and the critical point of this function.