On Bivariate Birnbaum–Saunders Distribution

SYNOPTIC ABSTRACT

Univariate Birnbaum–Saunders distribution has been used quite effectively to analyze positively skewed lifetime data. It has received considerable amount of attention in the last few years. In this study, we discuss the bivariate Birnbaum–Saunders distribution from a reliability and dependence point of view. It is observed that the bivariate Birnbaum–Saunders distribution can be obtained as a Gaussian copula. It helps in deriving several dependency properties and also in computing several dependency measures of the bivariate Birnbaum–Saunders distribution. Further, we consider the estimation of the unknown parameters based on copula and study their performances using Monte Carlo simulations. One dataset has been analyzed for illustrative purposes. Finally, we extend some of the results for multivariate Birnbaum–Saunders distribution also.

KEY WORDS AND PHRASES:

• Birnbaum–Saunders distribution
• copula
• hazard gradient
• maximum likelihood estimators
• total positivity

Acknowledgments

The authors would like to thank the referees for their constructive suggestions.