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From Sébastien Brisard <sebastien.bris...@m4x.org>
Subject Re: [math] Distributions over sample spaces other than R
Date Wed, 02 Nov 2011 07:08:09 GMT
>
> What exactly do we gain by having the common parent?  The inverse
> cdf machinery will work only for the continuous (by that, I mean
> real-valued RV) case.  Note how it is overriden now in
> AbstractIntegerDistribution.  So why not just leave that alone and
> separate out the discrete/integer/whatever-we-want-to-call-it case?
> Discrete distributions are fundamentally different.  They have
> pmfs.  They have discrete value sets.  Inversion works differently.
> Inequalities work differently.  Why not just cleanly separate?
>
> Phil
>
I agree with Phil: do we have a use-case where this common parent
would be required?
This common parent would be very satisfactory on the theoretical side,
but in my view, in order to be really beneficial, it would have to
provide a unified way to access to the *probability measure*. So, in
order to accomodate both discrete and continuous cases, this would
require to implement the pdf/pmf as a measure. Instead of
density(double x), we would have to provide a method
integrate(UnivariateRealFunction f) which would return the integral of
f against the probability measure. While doable, and beautiful from
the mathematical point of view, I'm wondering about the
usefulness/efficiency.

Sébastien

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