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2017 Partition structure and the $A$-hypergeometric distribution associated with the rational normal curve
Shuhei Mano
Electron. J. Statist. 11(2): 4452-4487 (2017). DOI: 10.1214/17-EJS1361

Abstract

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.

Citation

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Shuhei Mano. "Partition structure and the $A$-hypergeometric distribution associated with the rational normal curve." Electron. J. Statist. 11 (2) 4452 - 4487, 2017. https://doi.org/10.1214/17-EJS1361

Information

Received: 1 August 2016; Published: 2017
First available in Project Euclid: 17 November 2017

zbMATH: 1382.62005
MathSciNet: MR3724486
Digital Object Identifier: 10.1214/17-EJS1361

Subjects:
Primary: 62E15
Secondary: 13P25, 60C05

JOURNAL ARTICLE
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Vol.11 • No. 2 • 2017
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