The Parsimonious Gompertzian Mortality Parameters: Evidence From Advanced Actuarial Numerical Estimation Technique

Abstract

Efforts in obtaining distribution function which reasonably models life table functions have always constituted a major challenge in mortality construction and attempts with many estimating functions have not solved the problem. Numerous distribution functions have been experimented for this purpose but do not seem to be of interest because they are not parsimonious in actuarial representation and consequently could not adequately describe mortality table data. In order to overcome this problem, it is possible to estimate parameters by adopting less sophisticated mortality distribution functions. In traditional mortality models like Gompertz function, mortality rate increases exponentially as ages advance chronologically. The parametric estimation is meant to produce an estimated value of μ_x.

This work aims to estimate the Gompertzian mortality model parameters from a new numerical perspective. We present a parametrization that focuses on actuarial information based on Gompertzian mortality from indirect approach. The paper intends to develop an acceptable level of approximating the Gompertz model parameters for mortality rates. The objectives are to estimate (i) the level of mortality at initial age (ii) the rate of mortality increase across ages (iii) construct the modal age at death and (iv) the ageing rate. In order to compute the parameters, a numerical method that is more advanced than the traditional methods is adopted to demonstrate that the Gompertz model describes the behaviour of mortality trajectory with all its actuarial parameters.