Gompertz-Makeham law of mortality

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 Gompertz in 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 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).

ee also

* Ageing
* Biodemography
* Biodemography of human longevity
* Biogerontology
* Demography
* Gompertz curve
* Life table
* Maximum life span
* 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.


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Gompertz function — A Gompertz curve or Gompertz function, named after Benjamin Gompertz, is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period.:y(t)=ae^{be^{ctwhere * a is the… …   Wikipedia

  • Mortality rate — Crude death rate by country Mortality rate is a measure of the number of deaths (in general, or due to a specific cause) in a population, scaled to the size of that population, per unit time. Mortality rate is typically expressed in units of… …   Wikipedia

  • Benjamin Gompertz — (March 5, 1779 July 14, 1865, London, England), was a self educated mathematician, denied admission to university because he was Jewish. Nevertheless he was made Fellow of the Royal Society in 1819. Gompertz is today mostly known for his Gompertz …   Wikipedia

  • Biodemography of human longevity — Biodemography is a multidisciplinary approach, integrating biological knowledge (studies on human biology and animal models) with demographic research on human longevity and survival. Biodemographic studies are important for understanding the… …   Wikipedia

  • Senescence — refers to the biological processes of a living organism approaching an advanced age (i.e., the combination of processes of deterioration which follow the period of development of an organism). The word senescence is derived from the Latin word… …   Wikipedia

  • Demography — Sociology …   Wikipedia

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • Life table — 2003 US mortality table, Table 1, Page 1 In actuarial science, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die before his or her next …   Wikipedia

  • List of life extension-related topics — Following is a list of topics related to life extension: compactTOC NOTOC 0–9* 15 Global ChallengesA* Accelerated aging disease ** Bloom syndrome ** Cockayne s syndrome ** Progeria ** Werner s syndrome ** Xeroderma pigmentosum * Accident * ACE… …   Wikipedia

  • List of mathematics articles (G) — NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”