 Gompertz distribution

A positive, exponentially increasing hazard function $h(t)=q{e}^{\beta t}$ gives the survivor functionIts mean is ${\beta }^{-1}{e}^{q/\beta }{E}_1(q/\beta )$, where $E_1$ is the exponential integral. Unlike the exponential distribution, its future mean waiting time is not the reciprocal of its current hazard function.

The Gompertz distribution is a continuous probability distribution often used to model the time until an event occurs, particularly in survival analysis and reliability engineering. It is characterized by a cumulative distribution function (CDF) that describes the likelihood of the time until an event, such as failure or death, occurs.