Abstract
In this note are deduced two characterizations of normal distributions in the class NH of probability distributions on a plane whose densities admit diagonal expansions in series of Hermite polynomials and the marginal distributions are standardized and normal.
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Translated from Matematicheskie Zametkl, Vol. 20, No. 1, pp. 139–146, July, 1976.
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Romanovich, V.A., Lobaskina, N.V. Two characteristic properties of normal distributions in the class NH. Mathematical Notes of the Academy of Sciences of the USSR 20, 636–640 (1976). https://doi.org/10.1007/BF01152771
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DOI: https://doi.org/10.1007/BF01152771