Estimating Parameters of he Force of Mortality in Actuarial Studies

The two-parameter Weibull model and two-parameter Gompertz model are commonly used as survival time distributions in actuarial studies. The estimation of the parameters of these models is numer ically involved. We consider the estimation problem in a Bayesian framework and give the Bavesian 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 adaptive Bayesian procedure is compatible with the exact Bayesian procedure. In particular for large samples numerical integration for computing the exact Bayesian procedure is difficult. In both cases, noninformative generalized Bayes estimators and relevant adaptive noninformative Bayes estimators are also given. Some examples will be provided