Weibull Distribution

Notation:

$X \sim Weibull(\lambda, k)$

Probability Density Function:

$f(x)= \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x / \lambda)^k}$

where:

Mean:

$\mathrm{E}[X]=\mu=\lambda\Gamma(1+1/k)$

Variance:

$\mathrm{Var}[X]=\sigma^2=\lambda^2\left[ \Gamma \left(1+ \dfrac{2}{k} \right) - \left(\Gamma \left(1+\dfrac{1}{k} \right) \right)^2\right]$

References:

  1. Weibull Distribution - Wikipedia
  2. Weibull Distribution - Wolfram MathWorld