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From Phil Steitz <>
Subject Re: [math] Continuous Distribution
Date Sat, 29 Oct 2011 14:58:51 GMT
On 10/29/11 7:16 AM, cwinter wrote:
> Phil Steitz wrote:
>> 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
> Hi,
> I also wasn't sure about the interpretation of "continuous" in
> ContinuousDistribution for a while. But I was incertain whether the claim
> was that the cumulative distribution function should be continuous or the
> Distribution itself should be absolutely continuous, i.e. should have a
> probability density function. Since density(double) had been put to
> ContinuousDistribution I was sure that the scope was absolutely continuous
> distributions.
> However, when allowing a generalized functions like the delta distribution
> (unfortunately, the term "distribution" is overloaded in mathematics) as
> density, then any distribution would be a ContinuousDistribution (implying
> that there is no need for Distribution, and DiscreteDistribution would be a
> special case of ContinuousDistribution). Additionally, it is not possible to
> implement such a generalized function meaningfully in the current setting.
> Thus I vote for defining ContinuousDistribution to be the interface for
> absolutely continuous distribution. I'm fine with a "gap" between
> DiscreteDistribution and ContinuousDistribution, i.e. with successors of
> Distribution which neither implement DiscreteDistribution nor
> ContinuousDistribution.

Thinking about this some more, I agree.

> Best Regards,
> Christian
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