SOLVING NOT COMPLETELY INTEGRABLE QUANTILE PFAFFIAN DIFFERENTIAL EQUATIONS



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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 Pfaan 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.

About the authors

L.E. Melkumova

Samara State University

Author for correspondence.
Email: morenov.sv@ssau.ru

S. Ya. Shatskikh

Samara State University

Email: morenov.sv@ssau.ru

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Copyright (c) 2012 Melkumova L., Shatskikh S.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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