Beta Distribution for the Probability Distribution Calculator

Density Function. The Beta distribution has the probability density function:

f(x) = G(n+w)/[G(n)G(w)] * [xn-1 * (1-x)w-1]

0 < x < 1, n > 0, w > 0

where

G

(Gamma) is the Gamma function (of argument Alpha)

n, w

are the shape parameters

Distribution function. The Beta distribution function (the term distribution function was first introduced by von Mises, 1919) is related to the incomplete Beta function. For more information, see Pearson, 1968.

Beta. This field displays the current variate value for the Beta distribution. When you edit this value (either manually or with the microscrolls), Statistica computes the associated p-value for the distribution with the specified degrees of freedom.

p. This field displays the p-value computed from the specified variate value and degrees of freedom or you can enter a desired p-value (either manually or edit the existing value with the microscrolls) and compute the critical value for the specified degrees of freedom.

Shape1, Shape2. Specify here the shape parameters of the distribution, n and w, respectively. If one or both of these parameters are changed, then the p-value will be recomputed based on the respective variate value.