Definition:Weibull Distribution

Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R_{\ge 0}$.

$X$ is said to have a Weibull distribution it has probability density function:


 * $ \map {f_X} x = \alpha \beta^{-\alpha} x^{\alpha - 1} e^{-\paren {\frac x \beta}^\alpha}$

for $\alpha, \beta \in \R_{> 0}$.