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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2012, Issue 3/1(94), Pages 20–39 (Mi vsgu3)  
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Solving not completely integrable quantile Pfaffian differential equations

L. E. Melkumova, S. Ya. Shatskikh

Dept. of Theory Probability and Mathematical Statistics, Samara State University, Samara, 443011, Russian Federation
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Abstract: The present work deals with quantile Pfaffian differential equations which are constructed using two-dimensional conditional quantiles of multidimensional probability distributions. As it was shown in [3] in case when the initial probability distributions have reproducible conditional quantiles this kind of Pfaffian equations is completely integrable and the integral manifold is the conditional quantile of maximum dimension. In this paper we discuss properties of integral manifolds of maximum possible dimension for quantile Pfaffian equations which are not completely integrable. Manifolds of this type are described in terms of conditional quantiles of intermediate dimensions.
Keywords: multidimensional probability distributions, conditional quantile reproducibility, quantile Pfaffian equations, Darboux class of differential 1-forms, first integrals, manifolds of maximum dimensions, mixture distributions.
Received: 20.01.2012
Revised: 20.01.2012
Document Type: Article
UDC: 519.213+517.936
Language: Russian
Citation: L. E. Melkumova, S. Ya. Shatskikh, “Solving not completely integrable quantile Pfaffian differential equations”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, no. 3/1(94), 20–39
Citation in format AMSBIB
\Bibitem{MelSha12}
\by L.~E.~Melkumova, S.~Ya.~Shatskikh
\paper Solving not completely integrable quantile Pfaffian differential equations
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2012
\issue 3/1(94)
\pages 20--39
\mathnet{http://mi.mathnet.ru/vsgu3}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного университета. Естественнонаучная серия
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