Non-Normal Distributions - Extreme Value Distribution

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 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.

Applications

This distribution is often used to model extreme events, such as the size of floods, gust velocities encountered by airplanes, maxima of stock market indices over a given year, etc.; it is also often used in reliability testing, for example in order to represent the distribution of failure times for electric circuits (see Hahn and Shapiro, 1967).

Estimation

Statistica will compute maximum likelihood estimates for the two parameters of the extreme value distribution (see Evans, Hastings, and Peacock, 1993).