Generalized Beta Distribution

(cont prob. dist for equations)

Usage:

Beta4Dist (x, a, b, c, d)

Definition:

Be ((x - c) / (d - c), α, β)

where Be is the beta distribution

Parameters:

 c is lower endpoint     d is upper endpoint

Required:

α > 0     β > 0     d > c

Support:

c ⋜ x ⋜ d

This is a beta distribution that has been shifted and scaled, so that the pdf has nonzero values from x=c to x=d, instead of from x=0 to x=1.  

This distribution has great flexibility to approximately  fit almost any smooth, unimodal distribution with no tails (i.e., only nonzero over a finite range).