An extended Birnbaum–Saunders distribution: Theory, estimation, and applications

Abstract

Birnbaum and Saunders (1969a) pioneered a lifetime model which is commonly used in reliability studies. Based on this distribution, a new model called the gamma Birnbaum–Saunders distribution is proposed for describing fatigue life data. Several properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, density function of the order statistics, and their moments are derived. We discuss the method of maximum likelihood and a Bayesian approach to estimate the model parameters. The superiority of the new model is illustrated by means of three failure real data sets. We also propose a new extended regression model based on the logarithm of the new distribution. The last model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.

Keywords:

• Birnbaum–Saunders distribution
• Fatigue life distribution
• Gamma distribution
• Lifetime data
• Maximum likelihood estimation
• Regression model.

Mathematics Subject Classification:

• 62H10
• 62N01
• 62N02