Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Berry–Esseen theorem
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==Bibliography== {{refbegin}} * {{cite journal| first=Andrew C. | last=Berry | year=1941 | title=The Accuracy of the Gaussian Approximation to the Sum of Independent Variates | journal=Transactions of the American Mathematical Society | volume=49 | issue=1 | pages=122–136 | jstor=1990053| doi=10.1090/S0002-9947-1941-0003498-3 | doi-access=free}} * Durrett, Richard (1991). ''Probability: Theory and Examples''. Pacific Grove, CA: Wadsworth & Brooks/Cole. {{ISBN|0-534-13206-5}}. * {{cite journal | last = Esseen | first = Carl-Gustav | title = On the Liapunoff limit of error in the theory of probability | year = 1942 | journal = Arkiv för Matematik, Astronomi och Fysik | issn = 0365-4133 | volume = A28 | pages = 1–19 }} * {{cite journal | last = Esseen | first = Carl-Gustav | title = Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law | year = 1945 | journal = Acta Mathematica | volume = 77 | pages = 1–125 | doi = 10.1007/BF02392223 }} * {{cite journal | last = Esseen | first = Carl-Gustav | title = A moment inequality with an application to the central limit theorem | year = 1956 | journal = Skand. Aktuarietidskr. | volume = 39 | pages = 160–170 }} * Feller, William (1972). ''An Introduction to Probability Theory and Its Applications, Volume II'' (2nd ed.). New York: John Wiley & Sons. {{ISBN|0-471-25709-5}}. * {{cite journal | last1 = Korolev | first1 = V. Yu. | last2 = Shevtsova | first2 = I. G. | title = On the upper bound for the absolute constant in the Berry–Esseen inequality | year = 2010a | journal = Theory of Probability and Its Applications | volume = 54 | issue = 4 | pages = 638–658 | doi = 10.1137/S0040585X97984449 }} * {{cite journal | last1 = Korolev | first1 = Victor | last2 = Shevtsova | first2 = Irina | title = An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums | year = 2010b | journal = Scandinavian Actuarial Journal | volume = 2012 | issue = 2 | doi= 10.1080/03461238.2010.485370 | pages=1–25 | arxiv= 0912.2795| s2cid = 115164568 }} * Manoukian, Edward B. (1986). ''Modern Concepts and Theorems of Mathematical Statistics''. New York: Springer-Verlag. {{ISBN|0-387-96186-0}}. * Serfling, Robert J. (1980). ''Approximation Theorems of Mathematical Statistics''. New York: John Wiley & Sons. {{ISBN|0-471-02403-1}}. * {{cite journal | last = Shevtsova | first = I. G. | title = On the absolute constant in the Berry–Esseen inequality | year = 2008 | journal = The Collection of Papers of Young Scientists of the Faculty of Computational Mathematics and Cybernetics | issue = 5 | pages = 101–110 }} * {{cite journal | last = Shevtsova | author-link = Irina Shevtsova | first = Irina | title = Sharpening of the upper bound of the absolute constant in the Berry–Esseen inequality | year = 2007 | journal = Theory of Probability and Its Applications | volume = 51 | issue = 3 | pages = 549–553 | doi= 10.1137/S0040585X97982591 }} * {{cite journal | last = Shevtsova | first = Irina | title = An Improvement of Convergence Rate Estimates in the Lyapunov Theorem | year = 2010 | journal = Doklady Mathematics | volume = 82 | issue = 3 | pages = 862–864 | doi= 10.1134/S1064562410060062 | s2cid = 122973032 }} * {{cite arXiv | last = Shevtsova | first = Irina | title = On the absolute constants in the Berry Esseen type inequalities for identically distributed summands | year = 2011 | eprint = 1111.6554 | class = math.PR }} * {{cite journal | last = Shiganov | first = I.S. | title = Refinement of the upper bound of a constant in the remainder term of the central limit theorem | year = 1986 | journal = Journal of Soviet Mathematics | volume = 35 | pages = 109–115 | doi=10.1007/BF01121471 | issue=3 | s2cid = 120112396 | doi-access = free }} * {{cite journal | last = Tyurin | first = I.S. | title = On the accuracy of the Gaussian approximation | year = 2009 | journal = Doklady Mathematics | volume = 80 | issue = 3 | pages = 840–843 | doi=10.1134/S1064562409060155 | s2cid = 121383741 }} * {{cite journal | last = Tyurin | first = I.S. | title = An improvement of upper estimates of the constants in the Lyapunov theorem | year = 2010 | journal = Russian Mathematical Surveys | volume = 65 | issue = 3(393) | pages = 201–202 | doi = 10.1070/RM2010v065n03ABEH004688 | s2cid = 118771013 }} * {{cite journal | last = van Beek | first = P. | title = An application of Fourier methods to the problem of sharpening the Berry–Esseen inequality | year = 1972 | journal = Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete | volume = 23 | pages = 187–196 | doi=10.1007/BF00536558 | issue=3 | s2cid = 121036017 | doi-access = free }} * {{cite journal | last = Zolotarev | first = V. M. | title = A sharpening of the inequality of Berry–Esseen | year = 1967 | journal = Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete | volume = 8 | pages = 332–342 | doi=10.1007/BF00531598 | issue=4 | s2cid = 122347713 | doi-access = free }} {{refend}}
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)