George, E. Olusegun; Cheon, Kyeongmi; Yuan, Yilian; Szabo, Aniko On exchangeable multinomial distributions. (English) Zbl 1499.62406 Biometrika 103, No. 2, 397-408 (2016). Summary: 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. Cited in 2 Documents MSC: 62P10 Applications of statistics to biology and medical sciences; meta analysis 92B15 General biostatistics 60E05 Probability distributions: general theory 60G09 Exchangeability for stochastic processes 62F10 Point estimation Keywords:clustered multinomial data; finite exchangeable set; marginal compatibility; overdispersion Software:CorrBin; SAS/STAT; CRAN; R PDFBibTeX XMLCite \textit{E. O. George} et al., Biometrika 103, No. 2, 397--408 (2016; Zbl 1499.62406) Full Text: DOI