In this paper, a new class of survival distributions based on the model of dependent lives and proportional hazard rate family is introduced. This new family of bivariate survival models contains several bivariate lifetime models and is more flexible. The main purpose of this paper is to generalize this family of bivariate survival distributions of dependent lives so that more flexible models can be achieved. These new families of distributions are called the bivariate proportional hazard rate (BPHR) and the bivariate proportional hazard rate-geometric (BPHRG) families, respectively. It is also observed that, if θ = 1, then the BPHR family is a particular state of the BPHRG family. Several features of these new families of distributions such as the multivariate aging properties, the bivariate hazard gradient, and dependency structures are investigated. We design a flexible computational EM algorithm to calculate the maximum likelihood estimation of parameters. Also, several simulation studies are represented to evaluate the efficiency of the EM algorithm. Finally, we analyze three real datasets and compare the BPHRG models with the BPHR models.
On a New Class of Bivariate Survival Distributions Based on the Model of Dependent Lives and its Generalization,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/6