Definitions

# Type-1 Gumbel distribution

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

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

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).