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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1977, Volume 22, Issue 5, Pages 745–758 (Mi mz8096)

Inequalities for the distribution of a sum of functions of independent random variables

A. M. Zubkov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Let $\xi=\sum_{i_1,…,i_r=1}^nf_{i_1,…,i_r=1}(\zeta_{i_1,…,i_r=1})$ where $\zeta_1,…,\zeta_n$ are independent random variables and the $f_{i_1,…,i_r=1}$ are functions (e.g., taking the values 0 and 1). For cases when “almost all” the summands forming $\xi$ are equal to 0 with a probability close to 1, estimates from above and below are obtained for the quantity $\mathsf P\{\xi=0\}$, as well as upper estimates for the distance in variation between the distribution $\xi$, and the distribution of the “approximating” sum of independent random variables.

Full text: PDF file (784 kB)

English version:
Mathematical Notes, 1977, 22:5, 906–914

Bibliographic databases:

UDC: 519.2

Citation: A. M. Zubkov, “Inequalities for the distribution of a sum of functions of independent random variables”, Mat. Zametki, 22:5 (1977), 745–758; Math. Notes, 22:5 (1977), 906–914

Citation in format AMSBIB
\Bibitem{Zub77} \by A.~M.~Zubkov \paper Inequalities for the distribution of a~sum of functions of independent random variables \jour Mat. Zametki \yr 1977 \vol 22 \issue 5 \pages 745--758 \mathnet{http://mi.mathnet.ru/mz8096} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=471039} \zmath{https://zbmath.org/?q=an:0381.60018} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 5 \pages 906--914 \crossref{https://doi.org/10.1007/BF01098356}