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. I take it you do not mean a frequency
>distribution, at least not of the usual kind where the area (or mass)
>sums to N, but something that looks like a probability distribution,
>having weights that are between zero and one, but for which the weights
>do not sum to 1.00. If the sum is less than 1, either the weights are
>not probabilities or at least one category is missing from the
>distribution (or both), and in the absence of further information one
>cannot tell which is the case. If the sum is greater than one, either
>the weights are not probabilities or the categories are not disjoint (or
>both), and again one cannot tell.
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.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
