Rozkład gamma – Wikipedia, wolna encyklopedia

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

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

${\displaystyle {\frac {1}{\Gamma (k)\theta ^{k}}}x^{k-1}e^{-{\frac {x}{\theta }}}}$

${\displaystyle {\frac {\gamma (k,{\frac {x}{\theta }})}{\Gamma (k)}}}$

${\displaystyle k{\theta }}$

${\displaystyle {(k-1)}{\theta }{\text{ dla }}k\geqslant 1}$

${\displaystyle k{\theta ^{2}}}$

${\displaystyle {\frac {2}{\sqrt {k}}}}$

${\displaystyle {\frac {6}{k}}}$

${\displaystyle k+\ln \theta +\ln \Gamma (k)}$
${\displaystyle +(1-k)\psi (k)}$

${\displaystyle (1-{\,\theta \,t})^{-k}{\text{ dla }}t<{\frac {1}{\theta }}}$

${\displaystyle (1-{\,\theta \,i\,t})^{-k}}$

Weatherburn (1946)