Gamma Distribution for Probability-Probability Plots

The Gamma distribution has the probability density function:

f(x) = {1/[G(c)b]}*[(x-q)/b]c-1 *e[-(x-q)/b]

0 <= x, c > 0, b > 0



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


is the Shape parameter


is the Threshold (location) parameter


is the Scale parameter


is the base of the natural logarithm, sometimes called Euler's e (2.71...)

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

In general, if the observed points follow the Gamma distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.

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