A confirmation of the expected interval: Ab initio estimation technique of parsimonious Gompertz mortality parameters

Abstract

The Gompertz law states a functional relationship on exponential scale between instantaneous intensity and age. The objective is to first estimate the model parameters by using mortality data and then confirm the interval of validity for the estimated parameters. The parsimonious model is implicitly expressed in terms of age and level of mortality while the force of mortality is the dependent variable. Current contributions in actuarial literature have made it tractable to obtain life span from the actuarial point of view, making the life table invaluable analytical tool for insurers. Mortality functions which have been developed recently possess sophisticated actuarial techniques with many parameters hence they are very complex to estimate numerically making it difficult to fit to mortality data. In order to overcome this problem, we need to employ numerical algebraic method to estimate the appropriate values of model parameters and which may enable us fit the function to mortality data. In this paper, the direct algebraic method offers simpler perspective of approximating mortality parameter and was decomposed into systems of algebraic equations. We observed that mortality over all ages for males is lower than that of females while the initial mortality for male is higher than that of female. The R-language software was employed in the computation. In view of actuarial benchmarks, our results confirm that the values of and  for both males and females lie within the expected interval. (see PDF for further information).