On the hazard function of Birnbaum–Saunders distribution and associated inference

In this paper, we discuss the shape of the hazard function of Birnbaum–Saunders distribution. Specifically, we establish that the hazard function of Birnbaum–Saunders distribution is an upside down function for all values of the shape parameter. In reliability and survival analysis, as it is often of interest to determine the point at which the hazard function reaches its maximum, we propose different estimators of that point and evaluate their performance using Monte Carlo simulations. Next, we analyze a data set and illustrate all the inferential methods developed here and finally make some concluding remarks.