A-hypergeometric distributions and Newton polytopes
A-hypergeometric distributions and Newton polytopes
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A-超几何分布和牛顿多胞形
DOI：
10.1016/j.aam.2018.05.001
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发表时间：
2018
影响因子：
1.1
通讯作者：
A.
中科院分区：
文献类型：
--
作者：
Takayama;N.;Kuriki;S. and Takemura;A.
给出了任意A-超几何分布的参数商空间与矩空间之间的一个双射。利用完整梯度法和映射与迭代比例缩放的渐近等价性，提出了一种计算映射逆像的算法。该算法给出了统计学中条件极大似然估计问题的一种求解方法。超几何函数理论与统计学之间的相互作用使我们能够给出一些新的A-超几何多项式公式。
We give a bijection between a quotient space of the parameters and the space of moments for anyA-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient method and an asymptotic equivalence of the map and the iterative proportional scaling. The algorithm gives a method for solving a conditional maximum likelihood estimation problem in statistics. The interplay between the theory of hypergeometric functions and statistics allows us to give some new formulas forA-hypergeometric polynomials.