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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.
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Mathematical Notes, 1977, 22:5, 906–914
Bibliographic databases:
UDC:
519.2 Received: 03.03.1977
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
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\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
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=471039}
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\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 906--914
\crossref{https://doi.org/10.1007/BF01098356}
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