[Scipy-tickets] [SciPy] #767: Add the limiting gumbel distribution to genextreme distribution when shape c=0

SciPy scipy-tickets@scipy....
Fri Oct 31 04:42:10 CDT 2008


#767: Add the limiting gumbel distribution to genextreme distribution when shape
c=0
-------------------------+--------------------------------------------------
 Reporter:  pbrod        |       Owner:  somebody
     Type:  enhancement  |      Status:  new     
 Priority:  normal       |   Milestone:          
Component:  scipy.stats  |     Version:          
 Severity:  normal       |    Keywords:          
-------------------------+--------------------------------------------------
 The generalized extremevalue cumulative distribution in standard form [1]_
 is defined as:


 {{{
 F(x;c) = exp(-(1-c*x)**(1/c)) for c>0 and c<0
 }}}

 where c is the shape parameter.

 The limiting case as c->0 is the Gumbel cdf defined as

 {{{

 F(x;c=0) = exp(-exp(-x))

 }}}

 and is not implemented in the scipy.stats.distributions.genextreme
 distribution.

 To add this limiting case to scipy.stats.distributions.genextreme would
 greatly simplify statistical analysis. Through inference on the shape
 parameter, c,  the data themselves determine the most approprate type of
 tailbehavior and there is no need for making subjective a priori judgement
 of which individual extremevalue family to adopt.


 .. [1] Stuart Coles (2000),
 "An Introduction to Statistical Modeling of Extreme Values"

-- 
Ticket URL: <http://scipy.org/scipy/scipy/ticket/767>
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