On Complex Random Variables

Anwer Khurshid, Zuhair A. Al-Hemari, Shahid Kamal

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.


Keywords


Complex Variables, Multivariate

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.534

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Title

On Complex Random Variables

Keywords

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.


Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810