Emilia Athayde

Shape and change point analyses of the Birnbaum-Saunders-t 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-t (BS-t) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-t 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.

Modeling wind energy flux by a Birnbaum–Saunders distribution with an unknown shift parameter

In this paper, we discuss a Birnbaum–Saunders distribution with an unknown shift parameter and apply it to wind energy modeling. We describe structural aspects of this distribution including properties, moments, mode and hazard and shape analyses. We also discuss estimation, goodness of fit and diagnostic methods for this distribution. A computational implementation in R language of the obtained results is provided. Finally, we apply such results to two unpublished real wind speed data from Chile, which allows us to show the characteristics of this statistical distribution and to model wind energy flux.

About Birnbaum–Saunders Distributions Based on the Johnson System

In this article, we study Birnbaum–Saunders distributions based on the Johnson system including the case of a location-scale model. We mainly focus our attention on a four-parameter Birnbaum–Saunders distribution, since it contains all the versions presented here as particular cases. We describe structural aspects of this distribution considering its basic indicators, such as the density, distribution and quantile functions, as well as its properties, moments and shape and hazard analyses.