We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the co-occurrence probabilities of dummy variables required for categorical and ordinal variables, we propose a parsimonious parameterization for the Grassmann distribution that ensures the positivity of probability distribution. As an application of the proposed distribution, we develop a factor analysis for categorical and ordinal variables and show the validity of the model using a real dataset.

翻译：本文提出一种适用于分类与有序随机变量的多元概率分布。为此，我们采用格拉斯曼分布并结合分类与有序变量的虚拟编码。为实现分类与有序变量所需的虚拟变量共现概率，我们提出一种简洁的格拉斯曼分布参数化方法，确保概率分布的正定性。作为该分布的应用，我们开发了针对分类与有序变量的因子分析，并通过实际数据集验证了模型的有效性。