Beta (Generalized) Distribution In probability theory and statistics, the Beta distribution is a family of continuous probability distributions defined on the interval [0,1] parameterized by two non-negative shape parameters, typically denoted by alpha and beta.

This is a generalized version of the Beta distribution with dynamic interval defined by parameters min and max.

f(x,alpha,beta,min,max) =  ( ( ( (x-min)/(max-min) ) ^(alpha-1) )*(1-( (x-min)/(max-min) ) )^ (beta-1))/(Beta(alpha,beta)-min/(max-min) )

where Beta (the beta function) is a normalization constant to ensure that the total probability is 1 and has next formula  

Beta(alpha,beta) = integral from 0 to 1 of t^(alpha-1)*(1-beta)^(alpha-1) dt support [min ⇐ x ⇐ max]