# Extreme Value Distribution for the Probability Distribution Calculator

Density Function. 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

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...)

Distribution Function. The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Extreme Value distribution is:

F(x) = e**{-e[-(x-a)/b]}

V. This field displays the current variate value for the Extreme Value distribution. When you edit this value (either manually or with the microscrolls), Statistica computes the associated p-value for the specified parameters.

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

Location, Scale. Specify here the threshold and scale parameters of the distribution, a and b, respectively. If this parameter is changed, then the p-value will be recomputed based on the respective variate value.