Volume 28 - Article 9 | Pages 259–270

Gamma-Gompertz life expectancy at birth

By Trifon I. Missov

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Date received:25 Jan 2012
Date published:12 Feb 2013
Word count:1502
Keywords:gamma-Gompertz frailty model, hypergeometric function, life expectancy, life expectancy at birth
DOI:10.4054/DemRes.2013.28.9
Weblink:All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/
 

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 I. Missov - Max-Planck-Institut für Demografische Forschung, Germany [Email]

Other articles by the same author/authors in Demographic Research

» 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

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