Extreme Value Distribution (Type I, Gumbel)

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



is the location parameter


is the scale parameter


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. For a complete listing of all distribution functions, see Distributions and Their Functions.