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arXiv · 1404.1856

Sums of Possibly Associated Bernoulli Variables: The Conway-Maxwell-Binomial Distribution

Joseph B. Kadane
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Abstract

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 (COMB) distribution and its multivariate extension, the Conway-Maxwell Multinomial (COMM) distribution, gracefully model both positive and negative association. Sufficient statistics and a family of proper conjugate distributions are found. The relationship of this distribution to the exchangeable special case is explored, and two applications are discussed.

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Joseph B. Kadane. 2014-04-07. Sums of Possibly Associated Bernoulli Variables: The Conway-Maxwell-Binomial Distribution. https://arxiv.org/abs/1404.1856

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