Beta Distribution

Parameters: Minimum value (Min), Maximum value (Max), Alpha (α), Beta (β)

Formula:

Formula for beta distribution

for Min is less than or equal to x is less than or equal to Max

where:

Formula for beta distribution z term

where:

Formula for beta distribution beta function term

and where Γ is the Gamma function.

Method 1: Gamma Density Combination

Comment: The Beta variate is obtained from:

Formula for beta distribution beta variate

where u = Gamma (α, 1) and v = Gamma (β, 1).

Method 2: Rational Fraction Approximation method with a Newton Polish step

Comment: This method is used instead of Method 1 when Latin Hypercube sampling is in effect.