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

SciPy scipy-tickets@scipy....
Fri Oct 31 11:00:19 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       |   Resolution:
Keywords:               |
-------------------------+--------------------------------------------------
Comment (by josefpktd):

Looking at distributions.py, the comments before class
genextreme_gen(rv_continuous) say:
{{{
## Generalized Extreme Value
##  c=0 is just gumbel distribution.
##  This version does not accept c==0
##  Use gumbel_r for c==0
}}}

{{{
class gumbel_r_gen(rv_continuous):
def _pdf(self, x):
ex = exp(-x)
return ex*exp(-ex)
def _cdf(self, x):
return exp(-exp(-x))
}}}

Additionally there is also a left-skewed gumbel_r with:

{{{
def _cdf(self, x):
return 1.0-exp(-exp(x))
}}}

maybe a comment could be put in the extradocs of genextrem_gen to point to
gumbel_r for the special case.

A quick check:
{{{
>>> stats.genextreme.cdf([-0.5,0,1,2],0.00001)
array([ 0.19229604,  0.36787944,  0.6922019 ,  0.87342538])
>>> stats.gumbel_r.cdf([-0.5,0,1,2])
array([ 0.19229565,  0.36787944,  0.69220063,  0.87342302])
}}}

Josef

--
Ticket URL: <http://scipy.org/scipy/scipy/ticket/767#comment:1>
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