Gompertz

Gompertz is a surname associated with Benjamin Gompertz (1779–1865), a British mathematician and actuary, and with several mathematical models and laws named after him. In science, Gompertz designates the Gompertz function, the Gompertz law of mortality, and the Gompertz distribution, all used to describe growth, aging, and survival processes.

Benjamin Gompertz was born in London to a Jewish family and contributed to mathematics, actuarial science, and demography. In 1825 he proposed what became known as the Gompertz law of mortality, arguing that the mortality rate increases exponentially with age. He published his ideas in the Philosophical Magazine, influencing actuarial practices and demographic forecasting.

The Gompertz function is a sigmoidal growth curve defined by G(t) = a exp(-b exp(-c t)) with a, b, c > 0. It starts with rapid growth that slows over time, approaching an upper asymptote. It is used to model tumor growth, aging processes, and other biological growth phenomena where expansion decelerates.

The Gompertz distribution arises from a hazard function that increases with age and is used in survival analysis and reliability engineering. The Gompertz law of mortality is a demographic model for aging populations; the Gompertz–Makeham law extends it by including a constant age-independent mortality term.

The term remains widely used across biology, demography, and statistics to describe growth and aging phenomena.