Analytic Expressions and Plausible Approximations for Life Expectancy at Birth in Gamma-Gompertz Mortality Settings

Trifon I. Missov, Max Planck Institute for Demographic Research

In a population with Gamma-distributed individual frailty and Gompertz-distributed mortality the life-expectancy integral can be calculated analytically. The resulting expression is inversely proportional to the Gompertz mortality rate coefficient b. However it contains a Gaussian hypergeometric function, which can sometimes lead to computational difficulties. In order to avoid the latter, we derive simplifications in a number of special cases, as well as propose a general plausible approximation.