### Rayleigh Distribution

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The Rayleigh distribution is a special case of the Weibull distribution. For Rayleigh distributions, the parameter `beta` is fixed at 2. The density and distribution functions are given by:

`f(x) = 2/alpha ((x-a)/alpha)e^(-((x-a)/alpha)^2)`

`F(x) = 1-e^(-((x-a)/alpha)^2)`