Gompertz Distribution

The Gompertz distribution is a theoretical distribution of survival times. Gompertz (1825) proposed a probability model for human mortality based on the assumption that the "average exhaustion of a man's power to avoid death to be such that at the end of equal infinitely small intervals of time, he lost equal portions of his remaining power to oppose destruction which he had at the commencement of these intervals" (Johnson, Kotz, Balakrishnan, 1995, p. 25). The resultant hazard function:

r(x)=Bcx, for x <= 0, B > 0, c <= 1

is often used in Survival Analysis. See Johnson, Kotz, Balakrishnan (1995) for additional details.