On closed-form expressions to Gompertz-Makeham life expectancy

Fredy Castellares; Silvio C Patrício; Artur J Lemonte; Bernardo L Queiroz

doi:10.1016/j.tpb.2020.04.005

On closed-form expressions to Gompertz-Makeham life expectancy

Theor Popul Biol. 2020 Aug:134:53-60. doi: 10.1016/j.tpb.2020.04.005. Epub 2020 May 11.

Authors

Fredy Castellares¹, Silvio C Patrício¹, Artur J Lemonte², Bernardo L Queiroz³

Affiliations

¹ Departamento de Estatística, Universidade Federal de Minas Gerais, Belo Horizonte/MG, Brazil.
² Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal/RN, Brazil. Electronic address: arturlemonte@gmail.com.
³ Departamento de Demografia, Universidade Federal de Minas Gerais, Belo Horizonte/MG, Brazil.

PMID: 32407857
DOI: 10.1016/j.tpb.2020.04.005

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Adult
Humans
Life Expectancy*
Mortality*