[SciPy-User] Sampling from an arbitrary distribution.

[josef.pktd at gmail.com]

On Tue, Mar 29, 2016 at 7:10 PM, Andrew Nelson <andyfaff at gmail.com> wrote:
> Hi all,
> I wish to sample from an arbitrary probability density distribution. At the
> moment I don't have a functional form for the density distribution (so I'm
> not sure if I can subclass scipy.stats.rv_continuous)
>
> What I do have is an array containing (finely) histogrammed samples of the
> distribution. I found some pre-existing code
> (http://www.nehalemlabs.net/prototype/blog/2013/12/16/how-to-do-inverse-transformation-sampling-in-scipy-and-numpy/)
> which I successfully modified to deal with pre-histogrammed data.

I was very successful using linear interpolation for the ppf to
generate random samples, which corresponds to a histogram distribution
http://jpktd.blogspot.ca/2012/12/visual-inspection-of-random-numbers.html


>
> Q1: Can I still subclass scipy.stats.rv_continuous to sample from my
> arbitrary distribution? e.g. use the histogram to construct the object and
> refer to this histogram when overriding _pdf.

It's very inefficient to generate random numbers if only the pdf is
defined. The default generic approach uses ppf which needs cdf which
needs. So you would better also define cdf and ppf.


> Q2: If not, then is it worth adding functionality for this kind of sampling?
> Where would it belong scipy.stats or numpy.random?

It might not fit well into the current scipy.distribution setup
because that is mostly stateless. In this case it could be an
advantage to store the interpolation arrays. Or maybe the advantage is
not so large if creating the interpolator is cheap

A Histogram distribution would be the continuous analog to the
arbitrary finite number of points discrete distribution, so might fit
as well.

Josef

>
> A.
>
>
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