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Random Discrete Distributions

J. F. C. Kingman
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 37, No. 1 (1975), pp. 1-22
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2984986
Page Count: 22
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Random Discrete Distributions
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Abstract

It is impossible to choose at random a probability distribution on a countably infinite set in a manner invariant under permutations of that set. However, approximations to such a choice can be made by considering exchangeable probability measures on the class of probability distributions over a finite set, and letting the size of that set increase without limit. Under suitable conditions the resulting probabilities, when arranged in descending order, have non-degenerate limiting distributions. These apparently arcane considerations lead to rather concrete conclusions in certain problems in applied probability.

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