Abstract
Within the framework of the Malakhov method of the cumulant description of probability distributions, a covariance approximation of multidimensional densities and probability integrals is obtained in the form of a power series in the elements of the covariance matrix of random variables and the derivatives of their 1D integral distribution functions. The necessary and sufficient conditions under which the characteristic function of the covariance approximation is positively definite are analyzed. It is shown that it is reasonable to formulate these conditions in terms of searching for the admitted region for the restriction parameters of 1D probability distribution functions.
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Original Russian Text © L.V. Labunets, N.L. Lebedeva, M.Yu. Chizhov, 2012, published in Radiotekhnika i Elektronika, 2012, Vol. 57, No. 6, pp. 638–648.
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Labunets, L.V., Lebedeva, N.L. & Chizhov, M.Y. A cumulant approximation of a multidimensional probability distribution. J. Commun. Technol. Electron. 57, 577–587 (2012). https://doi.org/10.1134/S1064226912050063
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DOI: https://doi.org/10.1134/S1064226912050063