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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, Volume 11, Issue 3, Pages 517–525
DOI: https://doi.org/10.21638/spbu01.2024.308 (Mi vspua313) 		 
MATHEMATICS

On estimation of values of jumps for discrete distribution functions

A. N. Frolov

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (297 kB)
DOI: https://doi.org/10.21638/spbu01.2024.308
Abstract: We obtain new inequalities for values of jumps for discrete distribution functions. Values of jumps are bounded by linear combinations of a finite number of moments of the distributions. Obtained inequalities can be used for estimation of ranges for values of improbable jumps when frequencies are zero and are not interesting as estimators. We discuss relationships of derived inequalities with inequalities for probabilities of unions of events and the Caushy-Bunyakovski and Holder inequalities as well.
Keywords: Bonferroni inequalities, probabilities of unions of events, probabilities of combinations of events, Caushy-Bunyakovski inequality, Holder inequality, value of jump of distribution function.
Funding agency Grant number
Russian Science Foundation 23-21-00078
The research was funded by the Russian Science Foundation (project no. 23-21-00078).
Received: 22.11.2023
Revised: 16.02.2023
Accepted: 22.02.2024
Document Type: Article
UDC: 519.2
MSC: 60E15, 60F15
Language: Russian
Citation: A. N. Frolov, “On estimation of values of jumps for discrete distribution functions”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11:3 (2024), 517–525
Citation in format AMSBIB
\Bibitem{Fro24}
\by A.~N.~Frolov
\paper On estimation of values of jumps for discrete distribution functions
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2024
\vol 11
\issue 3
\pages 517--525
\mathnet{http://mi.mathnet.ru/vspua313}
\crossref{https://doi.org/10.21638/spbu01.2024.308}
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