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From Al Chou <>
Subject Re: [math] Questions regarding probability distributions
Date Wed, 20 Oct 2004 21:25:31 GMT
Hi, Frank,

--- F Norin <> wrote:
> > >Note: There are also distributions that are neither discrete, continuous
> > > or a mixture of the two. For example, there are numerous distributions
> > > based upon the Cantor ternary sets.
> >
> > Practical counter-examples like what you have above are more compelling ;-)
> Sure, a standard example of a Cantor ternary set distribution can be created 
> like this:
> Distributions like this are actually used in practical applications as 
> probability models within fields such as biophysics, molecular biology and 
> quantum mechanics.

Do you have any references for the quantum physics cases?  I certainly didn't
specialize in quantum physics (plasma physics typically uses almost everything
_but_ quantum physics), but I did get as far as a EE graduate course in QED and
never encountered such probability models.  Maybe it's because I wasn't in a
physics department or ever really encountered molecular models in what I was

Honestly, I doubt most of the users of Commons Math will be needing this kind
of distribution, but I guess if we merge in (parts of) Colt, we might end up
attracting that kind of user.  In any case, I learned something new today,
which is cool.


> [Proving that X is a probability distribution isn't exactly trivial- it 
> requires rather advanced concepts from measure theory, see Chung, "A course 
> in Probability Theory", Academic Press (1974), p.12-13, for a rigorous 
> treatment of this.] 
> > >but if you want a completely generic and typesafe definition you should
> > >go for something like
> > >
> > >public interface ProbabilityDistribution {
> > >        public Probability distributionFunction(Number x);
> > >}
> >
> > I think we can make it work with doubles and don't see a big loss there.  I
> > guess this is where I get off the bus ;-) -- though I see your point.
> Ok, but I do think there is a strong case for having a separate Probability 
> class.
> /Frank N

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