On closed-form expressions to Gompertz-Makeham life expectancy

Abstract

Missov and Lenart (2013) derived closed-form solutions to the life expectancy and remaining life expectancy at age x when the mortality is governed by a Gompertz-Makeham hazard, which is a parametric model commonly applied to human mortality data at adult and old ages. However, the closed-form expressions provided by these authors are not correct. We provide, therefore, valid and correct expressions using elementary calculus. We also consider numerical studies using real data to show that the formulas we provide deliver satisfactory results.

Keywords: Gamma Gompertz–Makeham distribution; Gompertz–Makeham distribution; Hypergeometric function; Life expectancy; Mortality.