Weibull

The density function of the Weibull distribution is

\[  f(x) = \alpha \beta ^{-\alpha }x^{\alpha - 1}e^{-(\frac{x}{\beta })^{\alpha }}  \]

for $x > 0$.

Parameters:

$\alpha $

is the shape parameter, $\alpha > 0$.

$\beta $

is the scale parameter, $\beta > 0$.