On 21 Nov 1999, Herman Rubin wrote:
> In article <[EMAIL PROTECTED]>,
> Donald F. Burrill <[EMAIL PROTECTED]> wrote:
> >On Thu, 18 Nov 1999, Alan Lewis wrote:
>
> >> I am looking for a reference on the use of the term
> >> "defective" for a probability distribution that does not
> >> have unit area. Is this a standard term?
>
> >Haven't seen any public responses to this one. I'd be inclined to doubt
> >that there is a well-defined term for "a probability distribution that
> >does not have unit area" since any such animal would not BE a
> >probability distribution....
>
> There is need for such a term. I believe that physicist
> allow their distributions to have such properties; the
> distribution of black body radiation gives not only the
> probability distribution given the total radiation, but
> also the total radiation.
>
> It would be useful to have this for other purposes; for
> example, the probability of an event would be the sum
> of its measures in the various "distributions". There
> is rarely any need to have distributions normalized
> during much of the process. Dividing to get probability
> distributions, and multiplying later to get the answers,
> does not seem to be profitable.
>
> Parts of the theory go through unchanged; one can talk
> about conditional measure, and it is a probability
> measure in all cases. However, independence gets down
> to probability in the first place.
>
Take a look at Chung's "a course in probability theory".
He has a section on "vague convergence", and makes use of the
idea of a "subprobability measure", which is precisely a
probability measure with total mass less than or equal to 1.
albyn
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http://www.reed.edu/~jones Albyn Jones [EMAIL PROTECTED]
Reed College, Portland OR 97202 (503)-771-1112 x7418
