# [SciPy-User] the skellam distribution

Johann Cohen-Tanugi cohen@lpta.in2p3...
Mon Nov 9 10:01:44 CST 2009

``` From what I understand of the initial statement from Ernest:
"
In case somebody is interested, or you want to include it
in scipy. I used these specs here from the R package:
cran.r-project.org/web/packages/skellam/skellam.pdf
"

he used the spec, as defined in this pdf, and did not look at the code
itself. If my interpretation of the small preamble above is correct, I
believe his implementation is not GPL-tainted, right?

Johann

Bruce Southey wrote:
> On 11/09/2009 08:40 AM, josef.pktd@gmail.com wrote:
>
>>
>>
>>> Hi,
>>>
>>> In case somebody is interested, or you want to include it
>>> in scipy. I used these specs here from the R package:
>>> cran.r-project.org/web/packages/skellam/skellam.pdf
>>>
>>> Note that I am no statician, somebody who knows what he's
>>> doing (as opposed to me ;) should verify it's correct.
>>>
>>>
>>> import numpy
>>> import scipy.stats.distributions
>>>
>>> # Skellam distribution
>>>
>>> ncx2 = scipy.stats.distributions.ncx2
>>>
>>> class skellam_gen(scipy.stats.distributions.rv_discrete):
>>>     def _pmf(self, x, mu1, mu2):
>>>         if x<  0:
>>>             px = ncx2.pdf(2*mu2, 2*(1-x), 2*mu1)*2
>>>         else:
>>>             px = ncx2.pdf(2*mu1, 2*(x+1), 2*mu2)*2
>>>         return px
>>>     def _cdf(self, x, mu1, mu2):
>>>         x = numpy.floor(x)
>>>         if x<  0:
>>>             px = ncx2.cdf(2*mu2, x*(-2), 2*mu1)
>>>         else:
>>>             px = 1-ncx2.cdf(2*mu1, 2*(x+1), 2*mu2)
>>>         return px
>>>     def _stats(self, mu1, mu2):
>>>         mean = mu1 - mu2
>>>         var = mu1 + mu2
>>>         g1 = (mu1 - mu2) / numpy.sqrt((mu1 + mu2)**3)
>>>         g2 = 1 / (mu1 + mu2)
>>>         return mean, var, g1, g2
>>> skellam = skellam_gen(a=-numpy.inf, name="skellam", longname='A Skellam',
>>>
>>>
>>>
>> Thanks, I think the distribution of the difference of two poisson
>> distributed random variables could be useful.
>>
>> Would you please open an enhancement ticket for this at
>> http://projects.scipy.org/scipy/report/1
>>
>> I had only a brief look at it so far, I had never looked at the
>> Skellam distribution before, and just read a few references.
>>
>> The "if x<  0 .. else ..." will have to be replace with a
>> "numpy.where" assignment, since the methods are supposed to work with
>> arrays of x (as far as I remember)
>>
>> _rvs could be implemented directly instead of generically (I don't
>> find the reference, where I saw it, right now).
>>
>> Documentation will be necessary,  a brief description in the
>> (currently) extradocs, and a listing of the properties for the
>> description of the distributions currently in the stats tutorial.
>>
>> I have some background questions, which address the limitation of the
>> implementation (but are not really necessary for inclusion into
>> scipy).
>>
>> The description in R mentions several implementation of Skellam. Do
>> you have a rough idea what the range of parameters are for which the
>> implementation using ncx produces good results? Do you know if any
>> other special functions would produce good results over a larger
>> range, e.g. using Bessel function?
>>
>> Wikipedia, http://en.wikipedia.org/wiki/Skellam_distribution , also
>> mentions (but doesn't describe) the case of Skellam distribution with
>> correlated Poisson distributions. Do you know what the difference to
>>
>> Tests for a new distribution will be picked up by the generic tests,
>> but it would be useful to have some extra tests for extreme/uncommon
>> parameter ranges. Do you have any comparisons with R, since you
>>
>>
>> Thanks again, I'm always looking out for new useful distributions,
>> (but I have to find the time to do the testing and actual
>> implementation).
>>
>> Josef
>>
>>
>>
>>
>>> Bye.
>>>
>>> --
>>> Ernest
>>> _______________________________________________
>>> SciPy-User mailing list
>>> SciPy-User@scipy.org
>>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>>
>>>
>>>
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>>
>>
>
> Generally any R code can not be used in numpy because R is GPL. Usually
> R code is also licensed under GPL  so translation from R to Python/numpy
> still maintains the original license. So the code not used by numpy
>
> You *must* show that you implementation is from a BSD-compatible source
> not from the R package. I can see that your code is very simple so there
> should be an viable alternative source.
>
> Also, in the _stats function why do you do not re-use the mean and var
> variables in computing the g1 and g2 variables?
>
> What are 'x, mu1, mu2' ?
> This looks like a scalar implementation so you need to either check that
> or allow for array-like inputs.
>
> Bruce
>
>
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>
>
```