Shape and change point analyses of the Birnbaum–Saunders-tt hazard rate and associated estimation

The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum–Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class of positively skewed models with lighter and heavier tails than the BS distribution. Particular cases of GBS distributions are the BS and BS-Student-tt (BS-tt) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-tt distribution. In addition, we evaluate the performance of the maximum likelihood and moment estimators of this change point using Monte Carlo methods. We also present an application with a real life data set useful for survival analysis, which shows the convenience of knowing such instant of change for establishing a reduction in the dose and, as a consequence, in the cost of the treatment.