[SciPy-User] the skellam distribution
Mon Nov 9 08:40:50 CST 2009
2009/11/8 Ernest Adrogué <email@example.com>:
> In case somebody is interested, or you want to include it
> in scipy. I used these specs here from the R package:
> 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
> 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)
> 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',
> shapes="mu1,mu2", extradoc="")
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
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
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
your implementation would be?
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
already looked it?
Thanks again, I'm always looking out for new useful distributions,
(but I have to find the time to do the testing and actual
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