Gompertz-Makeham law of mortality
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[[:pl:Prawo umieralności Makehama-Gompertza]]
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 Gompertz]] in [[1825]]) with [[exponential growth|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 rate|mortality]] before 1950s was mostly due to decrease in the age-independent mortality component ([[William Makeham|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 theory]] the 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 distribution]] for the negative of age, restricted to negative values for the [[random variable]] (positive values for age).
==See also==
* [[Ageing]]
* [[Biodemography]]
* [[Biodemography of human longevity]]
* [[Gerontology|Biogerontology]]
* [[Demography]]
* [[Gompertz curve]]
* [[Life table]]
* [[Maximum life span]]
* [[Mortality rate|Mortality]]
* [[Reliability theory of aging and longevity]]
==Further reading==
* [[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.
[[Category:Population]]
[[Category:Demography]]
[[Category:Death]]
[[Category:Aging]]
[[Category:Gerontology]]
[[Category:Actuarial science]]
[[Category:Statistical laws]]
[[fr:Modèle de Gompertz]]
[[pl:Prawo umieralności Makehama-Gompertza]]
[[pt:Lei de Gompertz-Makeham]]
[[ru:Распределение Гомпертца]]
[[uk:Закон смертності Ґомпертца-Мейкгама]]