On estimation of values of jumps for discrete distribution functions

Authors

  • Аndrei N. Frolov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

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

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Published

2024-10-15

How to Cite

Frolov А. N. (2024). On estimation of values of jumps for discrete distribution functions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(3), 517–525. https://doi.org/10.21638/spbu01.2024.308

Issue

Vol. 11 No. 3 (2024)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.