Covariance matrix formula for Birnbaum–Saunders regression models

Abstract

The Birnbaum–Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Keywords:

• asymptotic expansion
• Birnbaum–Saunders distribution
• covariance matrix
• fatigue life distribution
• lifetime data
• maximum-likelihood estimation

Acknowledgements

The author gratefully acknowledges grants from FAPESP (Brazil).