有理正态曲线的A-超几何分布与剖分结构
Partition structure and the A-hypergeometric distribution associated with the rational normal curve
摘要：
归一化常数为A-超几何多项式的分布称为A-超几何分布。这种分布又是边际和固定的列联表上的广义超几何分布的推广。在本文中，我们将看到，一个A-超几何分布与一个齐次矩阵的两行，特别是，与合理的正态曲线，出现在推论涉及可交换的划分结构。本文给出了一般（任意行数）A-超几何分布的精确抽样算法。然后讨论了有理正态曲线的A-超几何分布的极大似然估计，它是一个代数指数族。牛顿多胞形的信息几何对于分析满指数族和曲指数族是有用的。给出了计算A-超几何多项式的代数方法。
英文摘要：
A distribution whose normalization constant is an A-hypergeometric polynomial is called an A-hypergeometric distribution. Such a distribution is in turn a generalization of the generalized hypergeometric distribution on the contingency tables with fixed marginal sums. In this paper, we will see that an A-hypergeometric distribution with a homogeneous matrix of two rows, especially, that associated with the rational normal curve, appears in inferences involving exchangeable partition structures. An exact sampling algorithm is presented for the general (any number of rows) A-hypergeometric distributions. Then, the maximum likelihood estimation of the A-hypergeometric distribution associated with the rational normal curve, which is an algebraic exponential family, is discussed. The information geometry of the Newton polytope is useful for analyzing the full and the curved exponential family. Algebraic methods are provided for evaluating the A-hypergeometric polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
