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Entropy 2016, 18(11), 383; doi:10.3390/e18110383

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
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)
View Full-Text   |   Download PDF [774 KB, uploaded 26 October 2016]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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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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