Gompertz distribution
= Gompertz distribution
{c}
{title2=$h(t)=qe^{\beta t}$}
{wiki}
A positive, exponentially increasing <hazard function> $h(t)=qe^{\beta t}$ gives the <survivor function>
$$
S(t)=\exp\!\left[-\frac q\beta(e^{\beta t}-1)\right],\qquad q,\beta>0.
$$
Its 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>.