${\displaystyle \lambda }$ parametr położenia (liczba rzeczywista)
${\displaystyle \beta >0}$ parametr skali (liczba rzeczywista)

${\displaystyle x\in (-\infty$ ;+\infty )}

${\displaystyle {\frac {z\,\exp(-z)}{\beta }}}$
gdzie ${\displaystyle z=\exp \left[-{\frac {x-\lambda }{\beta }}\right]}$

${\displaystyle \exp(-\exp[-(x-\lambda )/\beta ])}$

${\displaystyle \lambda +\beta \,\gamma }$

${\displaystyle \lambda -\beta \,\ln(\ln(2))}$

${\displaystyle \lambda }$

${\displaystyle {\frac {\pi ^{2}}{6}}\,\beta ^{2}}$

${\displaystyle {\frac {12{\sqrt {6}}\,\zeta (3)}{\pi ^{3}}}\approx 1{,}14}$

${\displaystyle {\frac {12}{5}}}$

${\displaystyle \Gamma (1-\beta \,t)\,\exp(\lambda \,t)}$

${\displaystyle \Gamma (1-i\,\beta \,t)\,\exp(i\,\lambda \,t)}$