Generation of Over-Dispersed and Under-Dispersed Binomial Variates |
| |
Authors: | Hongshik Ahn James J. Chen |
| |
Affiliation: | Division of Biometry and Risk Assessment , National Center for Toxicological Research, Food and Drug Administration , Jefferson , Arkansas , 72079 , USA |
| |
Abstract: | 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. |
| |
Keywords: | Beta-binomial Correlated binary Intracluster correlation Monte Carlo Teratology |
|