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June 2016 Sums of Possibly Associated Bernoulli Variables: The Conway–Maxwell-Binomial Distribution
Joseph B. Kadane
Bayesian Anal. 11(2): 403-420 (June 2016). DOI: 10.1214/15-BA955


The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway–Maxwell-Binomial (CMB) distribution gracefully models both positive and negative association. This distribution has sufficient statistics and a family of proper conjugate distributions. The relationship of this distribution to the exchangeable special case is explored, and two applications are discussed.


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Joseph B. Kadane. "Sums of Possibly Associated Bernoulli Variables: The Conway–Maxwell-Binomial Distribution." Bayesian Anal. 11 (2) 403 - 420, June 2016.


Published: June 2016
First available in Project Euclid: 14 May 2015

zbMATH: 1357.60019
MathSciNet: MR3471996
Digital Object Identifier: 10.1214/15-BA955

Keywords: arithmetic binomial , beta-binomial , correlated Bernoulli random variables , correlated binomial , multiplicative binomial

Rights: Copyright © 2016 International Society for Bayesian Analysis

Vol.11 • No. 2 • June 2016
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