The study of semiparametric families is useful because it provides methods of extending families for adding flexibility in fitting data. The main aim of this paper is to introduce a class of bivariate semiparametric families of distributions. One especial bivariate family of the introduced semiparametric families is discussed in details with its sub-models and different properties. In most of the cases the joint probability distribution, joint distribution and joint hazard functions can be expressed in compact forms. The maximum likelihood and Bayesian estimation are considered for the vector of the unknown parameters. For illustrative purposes a data set has been re-analyzed and the performances are quite satisfactory. A simulation study is performed to see the performances of the estimators.
This paper presents a new generalization of the extended Gompertz distribution. We defined the so-called exponentiated generalized extended Gompertz distribution, which has at least three important advantages: (i) Includes the exponential, Gompertz, extended exponential and extended Gompertz distributions as special cases; (ii) adds two parameters to the base distribution, but does not use any complicated functions to that end; and (iii) its hazard function includes inverted bathtub and bathtub shapes, which are particularly important because of its broad applicability in real-life situations. The work derives several mathematical properties for the new model and discusses a maximum likelihood estimation method. For the main formulas related to our model, we present numerical studies that demonstrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the EGEG model. Three real- world data sets were used for applications in order to illustrate the usefulness of our proposal.