## Weibull Distribution

Note: For the mathematical formulas to display properly in this help file, please download and install the free MathPlayer. Once this is installed, refresh this topic. The page will then display the math formulas in blue text. Clicking on these formulas displays them in a slightly larger size.

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)`