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Posted to dev@commons.apache.org by Sébastien Brisard <se...@m4x.org> on 2011/10/29 06:31:03 UTC
[math] Continuous Distribution
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?
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,
Sébastien
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Re: [math] Continuous Distribution
Posted by Phil Steitz <ph...@gmail.com>.
On 10/29/11 7:16 AM, cwinter wrote:
> Phil Steitz wrote:
>> On 10/28/11 9:31 PM, Sébastien 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.
Phil
> Best Regards,
> Christian
>
>
> --
> View this message in context: http://apache-commons.680414.n4.nabble.com/math-Continuous-Distribution-tp3950057p3950916.html
> Sent from the Commons - Dev mailing list archive at Nabble.com.
>
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Re: [math] Continuous Distribution
Posted by cwinter <ch...@aol.com>.
Phil Steitz wrote:
>
> On 10/28/11 9:31 PM, Sébastien 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.
Best Regards,
Christian
--
View this message in context: http://apache-commons.680414.n4.nabble.com/math-Continuous-Distribution-tp3950057p3950916.html
Sent from the Commons - Dev mailing list archive at Nabble.com.
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Re: [math] Continuous Distribution
Posted by Phil Steitz <ph...@gmail.com>.
On 10/28/11 9:31 PM, Sébastien 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,
> Sébastien
>
> ---------------------------------------------------------------------
> To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
> For additional commands, e-mail: dev-help@commons.apache.org
>
>
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