Random Discrete Distributions
J. F. C. Kingmán · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1975
Summary 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.