From AMS Glossary
A continuous distribution having properties of nonnegativity and positive skewness often used in the atmospheric sciences, especially to model variations in wind speed.
Its probability distribution function (pdf) is given by
where α and β are the shape and scale parameters, respectively, that control the form of the Weibull distribution. For α = 1, the Weibull distribution is identical to the gamma distribution; for α = 3.6, the Weibull is very similar to the Gaussian distribution. The scale parameter β acts to either stretch or compress the basic shape of the distribution along the x axis for a given α.