Volume 32 - Article 36 | Pages 1031–1048

The Gompertz force of mortality in terms of the modal age at death

By Trifon I. Missov, Adam Lenart, Laszlo Nemeth, Vladimir Canudas-Romo, James Vaupel

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Date received:22 Jul 2014
Date published:20 May 2015
Word count:3030
Keywords:Gompertz force of mortality, Gumbel distribution, maximum likelihood, modal age at death, parameter correlation
Weblink:All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/


Background: The Gompertz force of mortality (hazard function) is usually expressed in terms of a, the initial level of mortality, and b, the rate at which mortality increases with age.

Objective: We express the Gompertz force of mortality in terms of b and the old-age modal age at death M, and present similar relationships for other widely-used mortality models. Our objective is to explain the advantages of using the parameterization in terms of M.

Methods: Using relationships among life table functions at the modal age at death, we express the Gompertz force of mortality as a function of the old-age mode. We estimate the correlation between the estimators of old (a and b) and new (M and b) parameters from simulated data.

Results: When the Gompertz parameters are statistically estimated from simulated data, the correlation between estimated values of b and M is much less than the correlation between estimated values of a and b. For the populations in the Human Mortality Database, there is a negative association between a and b and a positive association between M and b.

Conclusions: Using M, the old-age mode, instead of a, the level of mortality at the starting age, has two major advantages. First, statistical estimation is facilitated by the lower correlation between the estimators of model parameters. Second, estimated values of M are more easily comprehended and interpreted than estimated values of a.

Author's Affiliation

Trifon I. Missov - Syddansk Universitet, Denmark [Email]
Adam Lenart - Syddansk Universitet, Denmark [Email]
Laszlo Nemeth - Max-Planck-Institut für Demografische Forschung, Germany [Email]
Vladimir Canudas-Romo - Australian National University, Australia [Email]
James Vaupel - Syddansk Universitet, Denmark [Email]

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