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Mathematics 2019, 7(3), 263; https://doi.org/10.3390/math7030263

Computing the Moments of the Complex Gaussian: Full and Sparse Covariance Matrix

1
Department of Mathematics, University of Genova, 16146 Genova, Italy
2
Department de Castro Statistics, Collegio Carlo Alberto, 10122 Torino, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 11 January 2019 / Revised: 5 March 2019 / Accepted: 8 March 2019 / Published: 14 March 2019
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Abstract

Given a multivariate complex centered Gaussian vector Z = ( Z 1 , , Z p ) with non-singular covariance matrix Σ , we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed. View Full-Text
Keywords: Complex Gaussian Distribution; null moments; moment factorisation Complex Gaussian Distribution; null moments; moment factorisation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Fassino, C.; Pistone, G.; Rogantin, M.P. Computing the Moments of the Complex Gaussian: Full and Sparse Covariance Matrix. Mathematics 2019, 7, 263.

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