Death Where is Your Sting?: Evidence from the Makeham’s Curve of Death Callisthenics

Abstract

The curve of death rate represents an effective device in evaluating the modal age at death for the insured population evolving out of the instantaneous measure of the functional relationship  in a particular instant. Results in mortality analysis for a life-aged  are commonly examined but the generation of individual curves of death and gender comparisons of their corresponding auxiliary parameters under Makeham’s parsimonious parametric law are rarely investigated. In this paper, the algebraic method is adopted to measure the curve of death in both males and females using the 2020 survival data of the US actuarial surveillance area for both sexes. This paper attempts to arouse computational derivations using R software for further applications in life insurance valuations within the framework of our technique. The specific objectives were to estimate the sub-parameters of the Makeham’s law, to compute the individual survival function based on the sub-parameters as against interval estimate and to compute the individual curve of death. From the trajectories of the computed curve of death results, the modal age at death for male is roughly 87 years while that of female is 89.5 years. This difference accounts for the risk of exposure in male than in female. Although the female’s ageing rate C and the sub-parameters for female are higher than those of male, computational evidence from the results confirms that the male’s overall curve of death is correspondingly still higher than female’s curve of death.