Open AccessSOLVING NOT COMPLETELY INTEGRABLE QUANTILE PFAFFIAN DIFFERENTIAL EQUATIONS
Author(s) -
L. E. Melkumova,
S. Ya. Shatskikh
Publication year - 2012
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2012-18-3.1-20-39
Subject(s) - quantile , mathematics , integrable system , dimension (graph theory) , conditional expectation , pfaffian , quantile regression , conditional probability distribution , quantile function , mathematical analysis , probability distribution , pure mathematics , statistics , moment generating function
The present work deals with quantile Pfaan dierential 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 Pfaan equations which are not completely integrable. Manifolds of this type are described in terms of conditional quantiles of intermediate dimensions.