Beta Distribution for Probability-Probability Plots

The Beta distribution has the probability density function:

f(x) = G(n+w)/[G(n)G(w)] * [(x-q)n-1 * (s+q-x)w-1]/sn+w-1

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



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

n, w

are the Shape parameters


is the Threshold (location) parameter


is the Scale parameter

Compute from data. When you clear this check box (on the Probability-Probability Plots Quick and Advanced tab), you then need to specify the two Shape parameters n and w as well as the Threshold and Scale parameters q and s, respectively. When you select the Compute from data check box and specify the Threshold and Scale parameters (q and s, respectively), STATISTICA estimates both Shape parameters n and w from the data.

In general, if the observed points follow the Beta distribution with the respective parameters, then they will fall onto the straight line in the P-P plot. Note that you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.

Use Max. Likelihood. The Use Max. Likelihood check box is displayed when you select the Beta distribution on the Probability-Probability Plots - Advanced tab. When you select the check box, STATISTICA uses the maximum likelihood method to estimate the Shape parameters of the Beta distribution (see Evans, Hastings, & Peacock, 1993, for details). If the check box is cleared, then the method of matching moments is used.