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