$A$-Hypergeometric Distributions and Newton Polytopes
Classical Analysis and ODEs
2015-11-13 v2 Statistics Theory
Statistics Theory
Abstract
We give a bijection between a quotient space of the parameters and the space of moments for any -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 to solve a conditional maximum likelihood estimation problem in statistics. Our interplay between the theory of hypergeometric functions and statistics gives some new formulas of -hypergeometric polynomials.
Cite
@article{arxiv.1510.02269,
title = {$A$-Hypergeometric Distributions and Newton Polytopes},
author = {Nobuki Takayama and Satoshi Kuriki and Akimichi Takemura},
journal= {arXiv preprint arXiv:1510.02269},
year = {2015}
}