Extreme Value Distribution. The extreme value (Type I) distribution (the term first used by Lieblein, 1953) 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 location parameter
b    is the scale parameter
e    is the base of the natural logarithm, sometimes called Euler's e (2.71...)
This distribution is also sometimes referred to as the distribution of the largest extreme.

See also, Process Analysis.

The graphic above shows the shape of the extreme value distribution when the location parameter equals 0 and the scale parameter equals 1.