## Weibull Distribution

The Weibull distribution is the most flexible distribution. By varying the three parameters, the Weibull distribution can assume many diverse shapes. The parameter a controls the location of the distribution.

The parameter `alpha` controls the scale (i.e., can "stretch" the density function). The parameter `beta` affects the shape of the distribution. The density and distribution functions are given by:

`f(x) = beta/alpha ((x-a)/alpha)^(beta-1)e^(-((x-a)/alpha)^beta)`

`F(x) = 1-e^(-((x-a)/alpha)^beta)`