on complex random variables

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Abstract

In this paper, it is shown that a complex multivariate random variable Z = (Z1, Z2,..., Zp)',is a complex multivariate normal random variable of dimensionality p if and only if all nondegenerate complex linear combinations of Z have a complex univariate normal distribution. The characteristic function of Z 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 Z is Hermitian positive definite. Marginal distributions of Z 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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Khurshid, A., Al-Hemyari, 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

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