Shifted Gompertz distribution

The shifted Gompertz distribution is the distribution of the larger of two independent random variables one of which has an exponential distribution with parameter b {\displaystyle b} and the other has a Gumbel distribution with parameters η {\displaystyle \eta } and b {\displaystyle b} . In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution, the labelling can be considered as accurate.

Source: Wikipedia — Shifted Gompertz distribution (CC BY-SA 4.0)