Type-2 Gumbel distribution

In probability theory, the Type-2 Gumbel probability density function is f ( x | a , b ) = a b x − a − 1 e − b x − a {\displaystyle \ f(x|a,b)=a\ b\ x^{-a-1}\ e^{-b\ x^{-a}}\quad } for x > 0 . {\displaystyle \quad x>0~.} For 0 < a ≤ 1 {\displaystyle \ 0<a\leq 1\ } the mean is infinite.