# Type-1 Gumbel distribution

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

$f(x|a,b)= a b e^{-(b e^{-ax} + ax)}\,$

for

$-\infty < x < \infty.$

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

## References

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