Parameter estimation and threshold selection of Gompertz mortality law

The Gompertz law is a widely-used human mortality model, especially for old ages. In this paper, we propose a new parameter estimation method for the Gompertz mortality law based on the weighted least squares regression framework. Unlike other existing weight schemes, we derive a statistically appropriate weight structure using the delta method in the spirit of the Gauss-Markov theorem. In addition, we propose a new criterion to select the Gompertz threshold age, from which the Gompertz law starts, another important aspect in practice. The new criterion is designed with actuarial applications in mind. In particular, it identifies the threshold by minimizing the difference in the actuarial present value between the observed mortality and the estimated one. We illustrate our findings using the Korean assured mortality dataset and show that the proposed methods to find the Gompertz parameters and the threshold work well.