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Multivariate \(T\)-normal distributions in applied statistics. (English. Russian original) Zbl 0978.62044

J. Math. Sci., New York 103, No. 5, 556-567 (2001); translation from Statisticheskie Metody Otsenivaniya i Proverki Gipotez 1998, 43-64 (1998).
Summary: We study the family of so-called \(T\)-normal distributions, which includes the multivariate Gaussian distributions and those derived from them by arbitrary strictly monotone transformations of individual components. An attempt is made to give a quite thorough presentation of the theory of \(T\)-normal distributions and provide us with a series of appropriate statistical analysis procedures, together with some examples. In conclusion, various schemes of genesis of experimental data where the hypothesis about \(T\)-normality can be accepted are considered.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis
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