The generalised extreme value
distribution
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The generalised extreme value (or generalized extreme value)
distribution characterises the behaviour of ‘block maxima’ under certain
(somewhat restrictive) regularity conditions. See also Nematrian’s webpages
about Extreme Value
Theory (EVT).
Distribution name

Generalised
extreme value (GEV) distribution (for maxima)

Common notation


Parameters

= shape
parameter
= location
parameter
= scale
parameter

Domain


Probability density
function

where

Cumulative distribution
function


Mean

where is Euler’s constant, i.e.

Variance

Where

Skewness

where is
the Riemann zeta function, i.e. .

(Excess) kurtosis


Other comments

defines the tail behaviour
of the distribution. The subfamilies defined by (Type I),
(Type
II) and (Type III) correspond to the
Gumbel, Frechét and Weibull families
respectively.
An important special case when analysing threshold
exceedances involves (and normally ) and this
special case may be referred to as .

Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “gev”. For
details of other supported probability distributions see here.
NAVIGATION LINKS
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