The hazard rate function of the logistic Birnbaum-Saunders distribution: Behavior, associated inference, and application

Abstract

The hazard (failure) rate is a fundamental statistical indicator commonly used in both reliability and survival analyses. In practice, the hazard curve might exhibit a non-monotonic unimodal behavior. Thus, determining the highest point of the peak of a non-monotonic hazard function is indeed a point of interest in lifetime analysis. This study discusses the shape of the hazard function of the logistic Birnbaum-Saunders distribution and associate estimation. This model belongs to the generalized Birnbaum-Saunders family of positively skewed models with lighter and heavier tails than the conventional two-parameter Birnbaum-Saunders distribution. The latter model originated from a problem related to material fatigue, a phenomenon of interest in material sciences. In this paper, we establish that the hazard rate of the logistic Birnbaum-Saunders distribution is either unimodal or decreasing depending on the value of the shape parameter. We also estimate the critical value of the hazard rate, which is the highest point of the peak of the hazard function, using moment estimators. We perform extensive Monte Carlo simulations to examine estimation efficiency numerically; moreover, we analyze a data set for the sake of illustration.