- Gompertz-Makeham law of mortality
The Gompertz-Makeham law states that death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age. In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.) the age-independent mortality component is often negligible, and in this case the formula simplifies to a
Gompertz law of mortality(proposed by Benjamin Gompertzin 1825) with exponential increase in death rates with age.
The Gompertz-Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window of about 30-80 years. At more advanced ages the death rates do not increase as fast as predicted by this mortality law - a phenomenon known as the
late-life mortality deceleration.
Historical decline in human mortality before 1950s was mostly due to decrease in the age-independent mortality component (Makeham parameter), while the age-dependent mortality component (the Gompertz function) was surprisingly stable in history before 1950s. After that a new mortality trend has started leading to unexpected decline in mortality rates at advanced ages and '
de-rectangularization' of the survival curve.
In terms of
reliability theorythe Gompertz-Makeham law of mortality represents a failure law, where the hazard rate is a mixture of non-aging failure distribution, and the aging failure distribution with exponential increase in failure rates.
The Gompertz law is the same as a
Fisher-Tippett distributionfor the negative of age, restricted to negative values for the random variable(positive values for age).
Leonid A. Gavrilov& Natalia S. Gavrilova(1991), "The Biology of Life Span: A Quantitative Approach". New York: Harwood Academic Publisher, ISBN 978-3-7186-4983-9
* Gavrilov, L.A., Nosov, V.N. A new trend in human mortality decline: derectangularization of the survival curve. Age, 1985, 8(3): 93-93.
* Gavrilov, L.A., Gavrilova, N.S., Nosov, V.N. Human life span stopped increasing: Why? Gerontology, 1983, 29(3): 176-180. PMID 6852544
* Gompertz, B., (1825). "On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies". [http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-55920 "Philosophical Transactions of the Royal Society of London", Vol. 115 (1825)] pp. 513-585.
* Makeham, W. M. "On the Law of Mortality and the Construction of Annuity Tables." J. Inst. Actuaries and Assur. Mag. 8, 301-310, 1860.
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