Adaptive Bayes estimators for parameters of the Gompertz survival model

摘要

The two-parameter Gompertz model is a commonly used survival time distribution in actuarial science and reliability and life testing. The estimation of the parameters of this model is numerically involved. We consider the estimation problem in a Bayesian framework and give the Bayesian estimators of parameters in terms of single numerical integrations. We propose an adaptive Bayesian estimation procedure by putting a prior only on one parameter and finding the other parameter by minimizing the distance between empirical and parametric cumulative distribution functions. This easily computable (even for large samples) adaptive Bayesian procedure is compatible with the exact Bayesian procedure. In particular, numerical integration for computing the exact Bayesian procedure is difficult for large samples. Furthermore, for the no prior information situation, a noninformative adaptive Bayes procedure is given. Some examples of the proposed adaptive method along with a comparison with other existing methods are given. Monte Carlo simulation has been used to compare the existing procedures with the proposed procedures.