Type-1 Gumbel distribution

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


 * $$f(x|a,b)= a b \exp(-(b \exp(-ax) + ax))\,$$

for


 * $$-\infty < x < \infty$$.

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