# Type-1 Gumbel distribution

In probability theory, the Type-1 Gumbel distribution function is

${\displaystyle f(x|a,b)=ab\exp(-(b\exp(-ax)+ax))\,}$

for

${\displaystyle -\infty .

The distribution is mainly used in survival analysis (also known as duration analysis or event-history modelling).

## References

Taken from the gsl-ref_19.html#SEC309, used under GFDL.