EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES,KRAWTCHOUCK POLYNOMIALS,AND EHRENFEST URNS |
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Authors: | Persi Diaconis Robert Griffiths |
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Affiliation: | 1. Department of Statistics, Sequoia Hall, 390 Serra Mall, Stanford University, CA 94305‐4065, USA. e‐mail: diaconis@math.standford.edu;2. Department of Statistics, University of Oxford, 1 South Parks Rd, Oxford OX1 3TG, UK. e‐mail: griff@stats.ox.ac.uk |
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Abstract: | This paper derives characterizations of bivariate binomial distributions of the Lancaster form with Krawtchouk polynomial eigenfunctions. These have been characterized by Eagleson, and we give two further characterizations with a more probabilistic flavour: the first as sums of correlated Bernoulli variables; and the second as the joint distribution of the number of balls of one colour at consecutive time points in a generalized Ehrenfest urn. We give a self‐contained development of Krawtchouck polynomials and Eagleson’s theorem. |
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Keywords: | bivariate binomial distributions correlation sequences Ehrenfest urns Krawtchouk polynomials Lancaster distributions |
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