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From Phil Steitz <phil.ste...@gmail.com>
Subject Re: [math] Continuous Distribution
Date Sat, 29 Oct 2011 05:02:57 GMT
On 10/28/11 9:31 PM, S├ębastien Brisard wrote:
> Hi,
> The following question might sound stupid, but occured to me while
> thinking about MATH-692. So here goes. What was initially meant by
> "Continuous Distribution" (as in AbstractContinuousDistribution) ?
> My view on this is that the underlying random variable is defined by a
> *density*, which takes *continuous* arguments. But nothing prevents
> this density to be infinite at some *discrete* points (Dirac
> generalized function). Then the cumulative sum would be only piecewise
> C1.
> When these distributions were first implemented, was it intended to
> include this case?

We did not talk about these cases initially, but the intent was to
include all continuous distributions.  More specifically, we did not
mean to leave a gap - i.e., every distribution should be either
discrete or continuous, which means singular distributions need to
be allowed as continuous.

Phil
> I should add that this case is not purely academic: it is frequently
> met in the analysis of random heterogeneous materials (for example:
> assemblies of hard, monodisperse spheres of radius 0.5: some
> observables have such a singularity at r = 1).
>
> Best regards,
> S├ębastien
>
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