A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 63-76
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In this article we will define new inequalities, connecting some functionals of probability distribution functions. These inequalities are based on the strict convexity of functions that are used in functional definition. The starting point of of this article is the work “Cramér–von Mises distance: probabilistic interpretation, confidence intervals and neighbourhood of model validation” by Ludwig Baringhaus and Norbert Henze. In our article we provide a generalization of inequality obtained in probabilistic interpretation of the Cramér–von Mises distance. If equality holds there appears a chance to give characterization of some probability distribution functions. Considering this fact and a special character of functional, it is possible to create a class of free-of-distribution two sample tests.
@article{ZNSL_2018_474_a3,
author = {I. V. Volchenkova and L. B. Klebanov},
title = {A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {63--76},
year = {2018},
volume = {474},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a3/}
}
TY - JOUR AU - I. V. Volchenkova AU - L. B. Klebanov TI - A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests JO - Zapiski Nauchnykh Seminarov POMI PY - 2018 SP - 63 EP - 76 VL - 474 UR - http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a3/ LA - ru ID - ZNSL_2018_474_a3 ER -
%0 Journal Article %A I. V. Volchenkova %A L. B. Klebanov %T A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests %J Zapiski Nauchnykh Seminarov POMI %D 2018 %P 63-76 %V 474 %U http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a3/ %G ru %F ZNSL_2018_474_a3
I. V. Volchenkova; L. B. Klebanov. A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 63-76. http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a3/
[1] L. Baringhaus, N. Henze, “Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation”, J. Nonparametric Statistics, 2017, 1–23 | DOI | MR
[2] L. B. Klebanov, $\mathfrak{N}$-Distances and their Applications, Charles University in Prague, The Karolinum Press, 2005
[3] L. B. Klebanov, I. V. Volchenkova, A new convexity-based inequality, characterization of probability distributions and some free-of-distribution tests, 2018, 6 pp., arXiv: 1805.06483v1 | MR