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On Complex Random Variables

Pakistan Journal of Statistics and Operation Research

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Title On Complex Random Variables
Creator Khurshid, Anwer; Department of Mathematical and Physical Science
College of Arts and Sciences, University of Nizwa
Sultanate of Oman
Al-Hemari, Zuhair A.; Ministry of Higher Education
Sultanate of Oman
Kamal, Shahid; College of Statistical and Actuarial Sciences
University of the Punjab, Lahore, Pakistan
Subject Statistics
Complex Variables, Multivariate

Description In this paper, it is shown that a complex multivariate random variable  is a complex multivariate normal random variable of dimensionality if and only if all nondegenerate complex linear combinations of  have a complex univariate normal distribution. The characteristic function of  has been derived, and simpler forms of some theorems have been given using this characterization theorem without assuming that the variance-covariance matrix of the vector  is Hermitian positive definite. Marginal distributions of  have been given. In addition, a complex multivariate t-distribution has been defined and the density derived. A characterization of the complex multivariate t-distribution is given. A few possible uses of this distribution have been suggested.
Publisher College of Statistical and Actuarial Sciences
Date 2012-07-01
Type info:eu-repo/semantics/article
Peer-reviewed Article
Format application/pdf
Source Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012; 645-654
Language eng