On exchangeable multinomial distributions
We derive an expression for the joint distribution of exchangeable multinomial random variables, which generalizes the multinomial distribution based on independent trials while retaining some of its important properties. Unlike de Finneti's representation theorem for a binary sequence, the exchangeable multinomial distribution derived here does not require that the finite set of random variables under consideration be a subset of an infinite sequence. Using expressions for higher moments and correlations, we show that the covariance matrix for exchangeable multinomial data has a different form from that usually assumed in the literature, and we analyse data from developmental toxicology studies. The proposed analyses have been implemented in R and are available on CRAN in the CorrBin package.
George, E., Cheon, K., Yuan, Y., & Szabo, A. (2016). On exchangeable multinomial distributions. Biometrika, 103 (2), 397-408. https://doi.org/10.1093/biomet/asw009