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Generation of Over-Dispersed and Under-Dispersed Binomial Variates

Hongshik Ahn and James J. Chen
Journal of Computational and Graphical Statistics
Vol. 4, No. 1 (Mar., 1995), pp. 55-64
DOI: 10.2307/1390627
Stable URL: http://www.jstor.org/stable/1390627
Page Count: 10
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Generation of Over-Dispersed and Under-Dispersed Binomial Variates
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Abstract

This article proposes an algorithm for generating over-dispersed and under-dispersed binomial variates with specified mean and variance. The over-dispersed/under-dispersed distributions are derived from correlated binary variables with an underlying continuous multivariate distribution. Different multivariate distributions or different correlation matrices result in different over-dispersed (or under-dispersed) distributions. The over-dispersed binomial distributions that are generated from three different correlation matrices of a multivariate normal are compared with the beta-binomial distribution for various mean and over-dispersion parameters by quantile-quantile (Q-Q) plots. The two distributions appear to be similar. The under-dispersed binomial distribution is simulated to model an example data set that exhibits under-dispersed binomial variation.

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