توزیع مقدار حدی تعمیم‌یافته

${\displaystyle \mu \in [-\infty ,\infty ]\,}$ محل (حقیقی)
${\displaystyle \sigma \in (0,\infty ]\,}$ اندازه (حقیقی)

${\displaystyle \xi \in [-\infty ,\infty ]\,}$

${\displaystyle x>\mu -\sigma /\xi \,\;(\xi >0)}$
${\displaystyle x<\mu -\sigma /\xi \,\;(\xi <0)}$

${\displaystyle x\in [-\infty ,\infty ]\,\;(\xi =0)}$

${\displaystyle {\frac {1}{\sigma }}(1\!+\!\xi z)^{-1/\xi -1}e^{-(1\!+\!\xi z)^{-1/\xi }}}$

${\displaystyle z={\frac {x-\mu }{\sigma }}}$

${\displaystyle \mu -{\frac {\sigma }{\xi }}+{\frac {\sigma }{\xi }}g_{1}}$

${\displaystyle g_{k}=\Gamma (1-k\xi )}$