The Gompertz–Makeham law states that the death rate is the sum of an ageindependent component (the Makeham term) and an agedependent component (the 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 ageindependent mortality component is often negligible. In this case the formula simplifies to a Gompertz law of mortality. In 1825, Benjamin Gompertz proposed an 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 from about 30 to 80 years of age. At more advanced ages, death rates do not increase as fast as predicted by this mortality law – a phenomenon known as the latelife mortality deceleration.
The decline in human mortality before the 1950s was mostly due to a decrease in the ageindependent (Makeham) mortality component, while the agedependent (Gompertz) mortality component was surprisingly stable. Since the 1950s, a new mortality trend has started in the form of an unexpected decline in mortality rates at advanced ages and "derectangularization" of the survival curve.
In the language of reliability theory, the Gompertz–Makeham law of mortality represents a failure law, where the hazard rate is a mixture of the nonaging 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).
