Improved Birnbaum–Saunders inference under type II censoring

Abstract

The Birnbaum–Saunders distribution is useful for modeling reliability data. In this paper we obtain adjusted profile maximum likelihood estimators for the Birnbaum–Saunders distribution shape parameter under type II data censoring. We consider the adjustments to the profile likelihood function proposed by Barndorff-Nielsen (1983), Cox and Reid (1987), Fraser and Reid (1995), Fraser et al. (1999) and Severini (1998, 1999). We obtain modified profile likelihood ratio tests and also consider bootstrap-based inference. Interval estimation is addressed as well. Several bootstrap confidence intervals are considered. Monte Carlo simulation results on point estimation, interval estimation and hypothesis testing inference are reported. Finally, we present two applications that use real (not simulated) data.