On probabilities of moderate deviations for combinatorial sums

Authors

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

Abstract

We investigate the asymptotic behaviour of probabilities of moderate deviations for combinatorial sums. We find a zone in which tails of distributions of combinatorial sums have the same asymptotic behavior as that of the standard normal law. The combinatorial sums have dependent increments. It yields that the classical method of characteristic functions can not be applied. We use Esseen type bounds for combinatorial sums that have been obtained in author papers recently. We show that the zone of the normal convergence is close to the best one which is for the case of centered independent random variables. We consider the case of finite variations of summands. The case of infinite variations is discussed as well. Refs 34.

Keywords:

combinatorial central limit theorem, combinatorial sum, probabilities of moderate deviations, Esseen inequality

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Published

2015-02-01

How to Cite

Frolov, A. N. (2015). On probabilities of moderate deviations for combinatorial sums. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(1), 60–67. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11131

Issue

Vol. 2 No. 1 (2015)

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.