PsiPearson6 Distribution

PsiPearson6 (a1,a2,β,...)

PsiPearson6 (α1, α2, β) is a distribution with a lower bound of 0, and a mode just beyond the lower bound.  The Pearson6 distribution is sometimes called the Beta distribution of the second kind.

If X1 ~ Gamma (α1,β) and X2 ~ Gamma (α2,1) are independent random variables, then X1/X2 has a Pearson6 distribution.   If X is a random variable with a Pearson6 (α1,α2,1) distribution, then X/(1+X) has a Beta (α1, α2) distribution.

Alternate Formulation:  PsiPerson6Alt

PsiPearson6Alt is the PsiPearson6 distribution defined through alternative arguments.  Two parameters are required and both must be chosen from the following list:  2 different percentiles, shape or scale.