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Journal Articles Physica A: Statistical Mechanics and its Applications Year : 2016

Predictive implications of Gompertz’s law


Gompertz’s law tells us that for humans above the age of 35 the death rate increases exponentially with a doubling time of about 10 years. Here, we show that the same law continues to hold up to age 106. At that age the death rate is about 50%. Beyond 106 there is so far no convincing statistical evidence available because the number of survivors are too small even in large nations. However, assuming that Gompertz’s law continues to hold beyond 106, we conclude that the mortality rate becomes equal to 1 at age 120 (meaning that there are 1000 deaths in a population of one thousand). In other words, the upper bound of human life is near 120. The existence of this fixed-point has interesting implications. It allows us to predict the form of the relationship between death rates at age 35 and the doubling time of Gompertz’s law. In order to test this prediction, we first carry out a transversal analysis for a sample of countries comprising both industrialized and developing nations. As further confirmation, we also develop a longitudinal analysis using historical data over a time period of almost two centuries. Another prediction arising from this fixed-point model, is that, above a given population threshold, the lifespan of the oldest persons is independent of the size of their national community. This prediction is also supported by empirical evidence.

Dates and versions

hal-01284930 , version 1 (08-03-2016)



Peter Richmond, Bertrand M. Roehner. Predictive implications of Gompertz’s law. Physica A: Statistical Mechanics and its Applications, 2016, 447, pp.446-454. ⟨10.1016/j.physa.2015.12.043⟩. ⟨hal-01284930⟩
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