There are three standard parameters for the Weibull distribution: Location, Scale, and Shape. The Location parameter is the lower bound for the variable.
The Shape parameter is a number greater than 0, usually a small number less than 10. When the Shape parameter is less than 3, the distribution becomes more and more positively skewed until it starts to resemble an exponential distribution (shape < 1). At a shape of 3.25, the distribution is symmetrical, and above that value, the distribution becomes more narrow and negatively skewed.
After you select the Location and Shape parameter, you can estimate the Scale parameter. The larger the scale, the larger the width of the distribution.
To calculate a more exact scale, estimate the mean and use the equation:
where (alpha) is the scale, (beta) is the shape, L is the location, and (gamma) is the gamma function. You can use the Microsoft Excel GAMMALN function and Microsoft Excel Solver to help you calculate this parameter.
For this distribution, there is a 63% probability that x falls between a and a+L.
Or estimate the mode and use the equation:
where (alpha) is the scale, (beta) is the shape, and L is the location.