Does the male’s parameters always exceed female’s parameters in a generally coexisting patterns of death under generalized Makeham’s mortality intensity?

Although the results in actuarial statistics and mortality analysis for (x) are currently being rediscovered, till now,  the generation of individual mortality rate and the comparison of gender-specific parameters within the framework of Makeham’s law remain inadvertently neglected. Mortality rate intensities serve as an effective tool for analyzing mortality levels within the insured population. These intensities are derived from the instantaneous measure of the probability of death at a specific moment, conditional upon survival up to that point. In this study, an algebraic method is employed to measure the mortality intensities of both males and females using survival data from the US actuarial surveillance area.  Further, this paper intends to stimulate computational derivations using R software for further use in pension and annuity applications within the framework of our algebraic technique. Consequently, the specific objectives are (i) to estimate the main parameters {A, B, C} of the Makeham’s law (ii) to compute the individual mortality rate intensity based on the parameters as against interval estimate (iii) to investigate if the disparity between the male and female parameters has significant effect on the overall mortality rates of either gender. From the trajectories of the computed mortality results, the mortality intensities of both gender exhibit same asymptotic behaviour along the x-axis initially and then smoothly rises exponentially around age 75. Consequently, the mortality law could not explain the decline in mortality. Although the ageing rate C of female is higher than that of men, computational evidence from our results confirms that the men’s overall mortality rate is correspondingly still higher than women’s mortality.