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).
![[SmartChart]](I/GEVDistribution_files/image001.gif)
![[SmartChart]](I/GEVDistribution_files/image002.gif)
![[SmartChart]](I/GEVDistribution_files/image003.gif)
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Distribution name
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Generalised
extreme value (GEV) distribution (for maxima)
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Common notation
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Parameters
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 = shape
parameter
 = location
parameter
 = scale
parameter
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Domain
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Probability density
function
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where
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Cumulative distribution
function
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Mean
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where  is Euler’s constant, i.e. 
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Variance
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Where 
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Skewness
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where  is
the Riemann zeta function, i.e.  .
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(Excess) kurtosis
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Other comments
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defines the tail behaviour
of the distribution. The sub-families 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  .
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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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