EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNS

Journal article

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. © 2012 Australian Statistical Publishing Association Inc.

Authors: Diaconis, P; Griffiths, R

• Publication status: Published
• Journal: AUSTRALIAN and NEW ZEALAND JOURNAL OF STATISTICS
• Volume: 54
• Issue: 1
• Pages: 81-101
• Publication date: 2012-03-01
• DOI: 10.1111/j.1467-842X.2012.00654.x
• EISSN: 1467-842X
• ISSN: 1369-1473
• Language: English
• Keywords: correlation sequences; Lancaster distributions; Krawtchouk polynomials; bivariate binomial distributions; Ehrenfest urns