Volume 28 - Article 9 | Pages 259–270  

Gamma-Gompertz life expectancy at birth

By Trifon Missov

This article is part of the ongoing Special Collection 8 "Formal Relationships"

Abstract

Background: The gamma-Gompertz multiplicative frailty model is the most common parametric model applied to human mortality data at adult and old ages. The resulting life expectancy has been calculated so far only numerically.

Objective: Properties of the gamma-Gompertz distribution have not been thoroughly studied. The focus of the paper is to shed light onto its first moment or, demographically speaking, characterize life expectancy resulting from a gamma-Gompertz force of mortality. The paper provides an exact formula for gamma-Gompertz life expectancy at birth and a simpler high-accuracy approximation that can be used in practice for computational convenience. In addition, the article compares actual (life-table) to model-based (gamma-Gompertz) life expectancy to assess on aggregate how many years of life expectancy are not captured (or overestimated) by the gamma-Gompertz mortality mechanism.

Comments: A closed-form expression for gamma-Gomeprtz life expectancy at birth contains a special (the hypergeometric) function. It aids assessing the impact of gamma-Gompertz parameters on life expectancy values. The paper shows that a high-accuracy approximation can be constructed by assuming an integer value for the shape parameter of the gamma distribution. A historical comparison between model-based and actual life expectancy for Swedish females reveals a gap that is decreasing to around 2 years from 1950 onwards. Looking at remaining life expectancies at ages 30 and 50, we see this gap almost disappearing.

Author's Affiliation

• Trifon Missov - Syddansk Universitet, Denmark EMAIL

Other articles by the same author/authors in Demographic Research

Makeham mortality models as mixtures: Advancing mortality estimations through competing risks frameworks
Volume 51 - Article 18

Longevity à la mode: A discretized derivative tests method for accurate estimation of the adult modal age at death
Volume 50 - Article 11

The Gompertz force of mortality in terms of the modal age at death
Volume 32 - Article 36

Unobserved population heterogeneity: A review of formal relationships
Volume 31 - Article 22

Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models
Volume 24 - Article 19

Most recent similar articles in Demographic Research

The impact of the COVID-19 pandemic on mortality in Uruguay from 2020 to 2022
Volume 51 - Article 29    | Keywords: COVID-19, excess mortality, life expectancy, Uruguay

On the relationship between life expectancy, modal age at death, and the threshold age of the life table entropy
Volume 51 - Article 24    | Keywords: Gompertz law, life expectancy, lifespan variation, longevity, mode, mortality

Standardized mean age at death (MADstd): Exploring its potentials as a measure of human longevity
Volume 50 - Article 30    | Keywords: formal demography, life expectancy, mean age at death, mortality, standardization

How lifespan and life years lost equate to unity
Volume 50 - Article 24    | Keywords: life expectancy, life table entropy, life years lost, lifespan variation

Subnational contribution to life expectancy and life span variation changes: Evidence from the United States
Volume 50 - Article 22    | Keywords: decomposition methods, life expectancy, lifespan variation, subnational mortality