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Open AccessArticle

Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones

Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Entropy 2016, 18(11), 383; https://doi.org/10.3390/e18110383
Received: 16 September 2016 / Revised: 19 October 2016 / Accepted: 20 October 2016 / Published: 26 October 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an application to maximum likelihood estimation for a certain exponential family over a cone of this class. View Full-Text
Keywords: convex cone; homogeneous cone; graphical model; Koszul–Vinberg characteristic function convex cone; homogeneous cone; graphical model; Koszul–Vinberg characteristic function
MDPI and ACS Style

Ishi, H. Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones. Entropy 2016, 18, 383.

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