Geodesic
Construction of multivariate probability distributions with fully reproducible conditional quantiles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 29-45

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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
Mots-clés : Pfaffian equation. 
@article{IVM_2020_11_a2,
     author = {L. E. Melkumova},
     title = {Construction of multivariate probability distributions with fully reproducible conditional quantiles},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--45},
     publisher = {mathdoc},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_11_a2/}
}
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L. E. Melkumova. Construction of multivariate probability distributions with fully reproducible conditional quantiles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 29-45. http://geodesic.mathdoc.fr/item/IVM_2020_11_a2/