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

被引：10

作者：

Diaconis, Persi ^{[2
]}

Griffiths, Robert ^{[1
]}

机构：

[1] Univ Oxford, Dept Stat, Oxford OX1 3TG, England

[2] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

来源：

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS | 2012年 / 54卷 / 01期

基金：

美国国家科学基金会;

关键词：

bivariate binomial distributions; correlation sequences; Ehrenfest urns; Krawtchouk polynomials; Lancaster distributions; BIVARIATE DISTRIBUTIONS; EXPANSIONS; THEOREM;

D O I：

10.1111/j.1467-842X.2012.00654.x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Eaglesons theorem.

引用

页码：81 / 101

页数：21

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