The generalised extreme value
distribution
[this page | pdf | back links]
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)
Distribution name
|
Generalised
extreme value (GEV) distribution (for maxima)
|
Common notation
|
![](I/GEVDistribution_files/image004.png)
|
Parameters
|
= shape
parameter
= location
parameter
= scale
parameter
|
Domain
|
![](I/GEVDistribution_files/image008.png)
|
Probability density
function
|
![](I/GEVDistribution_files/image009.png)
where
![](I/GEVDistribution_files/image010.png)
|
Cumulative distribution
function
|
![](I/GEVDistribution_files/image011.png)
|
Mean
|
![](I/GEVDistribution_files/image012.png)
where is Euler’s constant, i.e. ![](I/GEVDistribution_files/image014.png)
|
Variance
|
![](I/GEVDistribution_files/image015.png)
Where ![](I/GEVDistribution_files/image016.png)
|
Skewness
|
![](I/GEVDistribution_files/image017.png)
where is
the Riemann zeta function, i.e. .
|
(Excess) kurtosis
|
![](I/GEVDistribution_files/image020.png)
|
Other comments
|
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 .
|
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
Contents | Prev | Next