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QUESTION: extension of binomial coefficient to real values
Posted:
Dec 6, 1996 4:40 AM
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Dear all,
I have a problem which I feel sure someone must have addressed before. I have
a statistic which I compute on a matrix A of observations. This requires that
I compute "a_{ij} choose 2" for each matrix element. For any real observation
matrix, all the elements are integers, so this presents no problem.
I also want to compute an expected value for this statistic. I know how to
compute the expected value of each matrix element, but these are then no
longer integers. Is there a sensible way to compute "a_{ij} choose 2" when
a_{ij} is not an integer? (I suspect that gamma functions may be the answer).
The expected a_{ij} are guaranteed to be rational, so at the moment I am doing the
calculation for the integer values obtained by multiplying by the common denominator,
and rescaling the result using the known maximum value for the implied sample
size. Does this sound reasonable?
Thanks for any thoughts,
David
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David Squire
Centre Universitaire d'Informatique, UniversitÃÂé de GenÃÂève.
Swiss Home Page: http://cuiwww.unige.ch/~squire/
Australian Home Page: http://www.cs.curtin.edu.au/~squizz/
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