Gamma Distribution
Notation:
$X \sim Gamma(k, \theta)$
Probability Density Function:
$f(x)=\dfrac{1}{\Gamma(k)\theta^k} x^{k-1}
e^{-x/\theta}$
where:
- $k > 0$ shape
- $\theta > 0$ scale
- $x > 0$
Mean:
$\mathrm{E}[X]=\mu=k\theta$
Variance:
$\mathrm{Var}[X]=\sigma^2=k\theta^2$
Alternative Parameterizations:
-
$Gamma(\alpha, \beta)$ - where $\alpha = k$ is the shape parameter and $\beta = 1/\theta$
is the rate parameter
(see Wikipedia)
References:
-
Gamma Distribution - Wikipedia
-
Gamma Distribution - Wolfram MathWorld