RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
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
\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}


Linking options:
  • http://mi.mathnet.ru/eng/mz8096
  • http://mi.mathnet.ru/eng/mz/v22/i5/p745

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:185
    Full text:90
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020