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On Complex Random Variables

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Author(s): Anwer Khurshid | Zuhair A. Al-Hemari | Shahid Kamal

Journal: Pakistan Journal of Statistics and Operation Research
ISSN 1816-2711

Volume: 8;
Issue: 3;
Date: 2012;
Original page

Keywords: Complex Variables | Multivariate

ABSTRACT
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.
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