Extreme Value (Gumbel) Distribution for Probability-Probability Plots

The extreme value (Type I) distribution has the probability density function:

f(x) = 1/b * e-(x-a)/b * e**[-e-(x-a)/b]

-∞ < x < ∞b > 0



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 Threshold and Scale parameters (a and b, respectively). When you select the check box, STATISTICA estimates the Threshold parameter a and the Scale parameter b from the data.

In general, if the observed points follow the Extreme Value 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.