Rozkład Weibulla

${\displaystyle \lambda >0}$ parametr skali (liczba rzeczywista)
${\displaystyle k>0}$ parametr kształtu (liczba rzeczywista)

${\displaystyle x\in [0;+\infty )}$

${\displaystyle (k/\lambda )(x/\lambda )^{(k-1)}e^{-(x/\lambda )^{k}}}$

${\displaystyle 1-e^{-(x/\lambda )^{k}}}$

${\displaystyle \lambda \Gamma \left(1+{\frac {1}{k}}\right)}$

${\displaystyle \lambda (\ln 2)^{1/k}}$

${\displaystyle \lambda \left({\frac {k-1}{k}}\right)^{\frac {1}{k}}}$ dla ${\displaystyle k>1}$

${\displaystyle \lambda ^{2}\Gamma \left(1+{\frac {2}{k}}\right)-\mu ^{2}}$

${\displaystyle {\frac {\Gamma (1+{\frac {3}{k}})\lambda ^{3}-3\mu \sigma ^{2}-\mu ^{3}}{\sigma ^{3}}}}$

${\displaystyle {\tfrac {-6\Gamma _{1}^{4}+12\Gamma _{1}^{2}\Gamma _{2}-3\Gamma _{2}^{2}-4\Gamma _{1}\Gamma _{3}+\Gamma _{4}}{[\Gamma _{2}-\Gamma _{1}^{2}]^{2}}}}$

${\displaystyle \gamma \left(1\!-\!{\frac {1}{k}}\right)+\ln \left({\frac {\lambda }{k}}\right)+1}$

Waloddi Weibull (1939, 1951)