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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

Article Details

How to Cite
Khurshid, A., Al-Hemari, Z. A., & Kamal, S. (2012). On Complex Random Variables. Pakistan Journal of Statistics and Operation Research, 8(3), 645-654. https://doi.org/10.18187/pjsor.v8i3.534