Modeling Sums of Exchangeable Binary Variables

17 Pages Posted: 28 Aug 2020

See all articles by Ryan Elmore

Ryan Elmore

University of Denver - Daniels College of Business

Date Written: July 14, 2020

Abstract

We introduce a new model for sums of exchangeable Bernoulli random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform of a gamma distribution function. Using Monte Carlo methods, we show that this new model compares favorably to the beta-binomial model with respect to estimating the success probability of the Bernoulli trials and the correlation between any two variables in the exchangeable set. We apply the new methodology to two classic data sets and the results are summarized.

Keywords: exchangeable binary variables, over-dispersion

Suggested Citation

Elmore, Ryan, Modeling Sums of Exchangeable Binary Variables (July 14, 2020). Available at SSRN: https://ssrn.com/abstract=3651494 or http://dx.doi.org/10.2139/ssrn.3651494

Ryan Elmore (Contact Author)

University of Denver - Daniels College of Business ( email )

2101 S. University Blvd.
Denver, CO 80208
United States

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