A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications

Abstract

We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum–Saunders–Poisson random variable. For censored data, we estimate the parameters of the regression model using maximum likelihood. We investigate the accuracy of the maximum likelihood estimates using Monte Carlo simulations. The importance of the proposed models, when compared to existing models, is illustrated by means of two real data sets.