The choice of an appropriate bivariate parametrical probability distribution for pairs of lifetime data in presence of censored observations usually is not a simple task in many applications. Each existing bivariate lifetime probability distribution proposed in the literature has different dependence structure. Commonly existing classical or Bayesian discrimination methods could be used to discriminate the best among different proposed distributions, but these techniques could not be appropriate to say that we have good fit of some particular model to the data set. In this paper, we explore a recent dependence measure for bivariate data introduced in the literature to propose a graphical and simple criterion to choose an appropriate bivariate lifetime distribution for data in presence of censored data.
In this paper a new two-parameter distribution is proposed. This new model provides more flexibility to modeling data with increasing and bathtub hazard rate function. Several statistical and reliability properties of the proposed model are also presented in this paper, such as moments, moment generating function, order statistics and stress-strength reliability. The maximum likelihood estimators for the parameters are discussed as well as a bias corrective approach based on bootstrap techniques. A numerical simulation is carried out to examine the bias and the mean square error of the proposed estimators. Finally, an application using a real data set is presented to illustrate our model.