A Generalized Gompertz Distribution with Hazard Power Parameter and Its Bivariate Extension: Properties and Applications

Recently, a new class of distributions, named bivariate hazard power parameter family of distributions is introduced. In this paper, a generalized Gompertz distribution is introduced as a member of this family in both univariate and bivariate cases. Different properties are discussed as moments and moment generating function. It is observed that the joint probability density function and the joint survival function can be expressed in explicit forms. Maximum likelihood estimation is considered for the model unknown parameters. Asymptotic confidence intervals for the unknown parameters are evaluated. Some simulations have been performed to see the performances of the MLEs. Three real data sets are applied to this model for illustrative purposes.