This paper introduces a general class of multivariate distributions for rates and proportions on the basis of the multivariate elliptical distribution. We derive various general properties of this multivariate distribution. The model parameters are estimated using the maximum likelihood estimation method. In particular, we have considered parameter estimation in detail for two special cases of this multivariate family, using multivariate normal kernel and multivariate Student-$t$ kernel. Hypothesis testing inference for the correlation matrix on the basis of the likelihood ratio test statistic is also proposed. Empirical applications that employ real data are considered to illustrate the usefulness of the new class of multivariate distributions for rates and proportions in practice.

本文在多元椭圆分布的基础上，介绍了一类通用的比率和比例多元分布。我们推导出这种多元分布的各种一般性质。使用最大似然估计方法估计模型参数。特别是，我们已经详细考虑了这个多元族的两个特殊情况的参数估计，使用多元正态核和多元Student-$吨$核心。还提出了基于似然比检验统计量的相关矩阵的假设检验推断。使用真实数据的经验应用被认为是说明新类别的多变量分布在实际中对比率和比例的有用性。