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.
Perhaps you have some other situation in mind; but there seems to me
little reason to call such a thing a "defective" probability distribution
-- it is not a probability distribution at all. It might perhaps be an
incomplete probability distribution, if one or more categories have been
overlooked or lost, but one could only guess that this might be the case.
You might, I suppose, be referring to a continuous function that more or
less resembles a probability distribution in shape, but for which the
area under the curve is not equal to 1. Then ideas about categories do
not apply; but one still cannot tell whether the function itself is
somehow out to lunch, or merely needs to be multiplied by a suitable
constant (or possibly, I suppose, by a suitable function).
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
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