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Journal of Probability and Statistics
Volume 2014, Article ID 597630, 6 pages
http://dx.doi.org/10.1155/2014/597630
Research Article

Point-Symmetric Multivariate Density Function and Its Decomposition

Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba 278-8510, Japan

Received 13 December 2013; Revised 21 April 2014; Accepted 23 April 2014; Published 13 May 2014

Academic Editor: Chin-Shang Li

Copyright © 2014 Kiyotaka Iki and Sadao Tomizawa. 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.

Abstract

For a -variate density function, the present paper defines the point-symmetry, quasi-point-symmetry of order ( ), and the marginal point-symmetry of order and gives the theorem that the density function is -variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of order . The theorem is illustrated for the multivariate normal density function.