Abstract: The Gompertz distribution has many applications, particularly in medical and actuarial studies. However, there has been little recent work on the Gompertz in comparison with its early investigation. The problem of analyzing and estimating parameters of bivariate Gompertz distribution with shared frailty is of interest and the focus of this paper. We propose maximum likelihood estimation procedure for a bivariate survival model in which dependence is generated by a gamma distribution. We assume that the bivariate survival times follow bivariate Gompertz distribution and distribution of censoring variable is independent of the two life times. A search of the literature suggests there is currently no bivariate Gompertz distribution with shared frailty.
Keywords: Bivariate Gompertz distribution, censored sample, fisher information, gamma frailty, maximum likelihood estimators (MLE), survival times