A Geometric Approach to Average Problems on Multinomial and Negative Multinomial Models

This paper is concerned with the formulation and computation of average problems on the multinomial and negative multinomial models. It can be deduced that the multinomial and negative multinomial models admit complementary geometric structures. Firstly, we investigate these geometric structures by...

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Published inEntropy (Basel, Switzerland) Vol. 22; no. 3; p. 306
Main Authors Li, Mingming, Sun, Huafei, Li, Didong
Format Journal Article
LanguageEnglish
Published MDPI 08.03.2020
MDPI AG
Subjects
average problem
geometric midpoints
karcher mean
structure characterization
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Summary:This paper is concerned with the formulation and computation of average problems on the multinomial and negative multinomial models. It can be deduced that the multinomial and negative multinomial models admit complementary geometric structures. Firstly, we investigate these geometric structures by providing various useful pre-derived expressions of some fundamental geometric quantities, such as Fisher-Riemannian metrics, α -connections and α -curvatures. Then, we proceed to consider some average methods based on these geometric structures. Specifically, we study the formulation and computation of the midpoint of two points and the Karcher mean of multiple points. In conclusion, we find some parallel results for the average problems on these two complementary models.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e22030306