PsiRayleigh (β) is a distribution with a finite lower bound of 0, a special case of a Weibull distribution. The Rayleigh distribution can be used to model component lifetimes.
If X is a random variable with Rayleigh distribution with parameter β = 1, then X2 has a Chi Square distribution with parameter 2 (two degrees of freedom). If X and Y are independent normally distributed random variables with mean zero and variance σ2, then (X2+Y2)1/2 has a Rayleigh distribution with parameter σ. Thus, a Rayleigh distribution may be used to model the length of a two-dimensional vector whose components are independent and normally distributed.
Alternate Formulation: PsiRayleighAlt
PsiRayleighAlt is the PsiRayleigh distribution defined through alternative arguments. One parameters is required and must be chosen from the following list: percentile, var or mean.