Extreme Value (Gumbel) Distribution for Probability-Probability
Plots Extreme Value (Gumbel) Distribution for Probability-Probability
PlotsThe 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
where
|
a |
is the Threshold (location) parameter |
|
b |
is the Scale parameter |
|
e |
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.