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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 11, Pages 29–45
DOI: https://doi.org/10.26907/0021-3446-2020-11-29-45 (Mi ivm9624) 		 
Construction of multivariate probability distributions with fully reproducible conditional quantiles

L. E. Melkumovaab

a Mercury Development Samara, 110, b. 1, Avrory str., Samara, 443069 Russia
b Samara National Research University, 34 Moskovskoye high., Samara, 443086 Russia
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DOI: https://doi.org/10.26907/0021-3446-2020-11-29-45
Abstract: It's known that when a multivariate probability distribution has a «big» conditional quantile that is fully reproducible when narrowed to uni-variate quantiles, then the respective quantile differential equation is completely integrable. Yet the converse is not true in general. In this paper, we show that, provided that certain conditions are satisfied, from the given completely integrable quantile equation, one can construct a multivariate distribution with a fully reproducible «big» conditional quantile. The constructed probability distribution may differ from the original distribution. We will also give a generalization of this result that suggests a method of shifting from a $(n-1)$-dimensional distribution satisfying certain conditions to an $n$-dimensional distribution with a fully reproducible «big» conditional quantile.
Keywords: conditional quantile reproducibility, quantile differential equation, Pfaffian equation.
Received: 12.12.2019
Revised: 05.03.2020
Accepted: 25.03.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 11, Pages 23–38
DOI: https://doi.org/10.3103/S1066369X20110031
Bibliographic databases:
Document Type: Article
UDC: 519.213
Language: Russian
Citation: L. E. Melkumova, “Construction of multivariate probability distributions with fully reproducible conditional quantiles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 11, 29–45; Russian Math. (Iz. VUZ), 64:11 (2020), 23–38
Citation in format AMSBIB
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\paper Construction of multivariate probability distributions with fully reproducible conditional quantiles
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 11
\pages 29--45
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\crossref{https://doi.org/10.26907/0021-3446-2020-11-29-45}
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\jour Russian Math. (Iz. VUZ)
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\issue 11
\pages 23--38
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