The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function, named after Benjamin Gompertz),[1] which increases exponentially with age,[2] and an age-independent component (the Makeham term, named after William Makeham).

[3] In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.

In 1825, Benjamin Gompertz proposed an exponential increase in death rates with age.

The empirical magnitude of the beta-parameter is about .085, implying a doubling of mortality every .69/.085 = 8 years (Denmark, 2006).

The quantile function can be expressed in a closed-form expression using the Lambert W function:[8] 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).