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# Type-1 Gumbel distribution

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

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

for

${\displaystyle -\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).