On exchangeable multinomial distributions
推导了可交换多项随机变量的联合分布表达式，该分布推广了基于独立试验的多项分布，并保留了其重要性质。通过高阶矩和相关性分析，发现其协方差矩阵与文献中通常假设的形式不同，并应用于发育毒理学数据分析。
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.