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Informatika i Ee Primeneniya [Informatics and its Applications], 2011, Volume 5, Issue 3, Pages 64–66 (Mi ia160)  

This article is cited in 11 scientific papers (total in 11 papers)

On the Berry–Esseen type inequalities for poisson random sums

V. Yu. Korolevab, I. G. Shevtsovaab, S. Ya. Shorgina

a Institute for Problems of Informatics RAS
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
References:
Abstract: For the uniform distance between the distribution function $\Phi(x)$ of the standard normal random variable and the distribution function $F_\lambda(x)$ of the Poisson random sum of independent identically distributed random variables $X_1, X_2,\dots$ with finite third absolute moment, $\lambda>0$ being the parameter of the Poisson index, it is proved the inequality
$$ \sup_{x}|F_\lambda(x)-\Phi(x)|\le 0.4532\frac{\mathsf E|X_1-\mathsf E X_1|^3}{(\mathsf D X_1)^{3/2}\sqrt{\lambda}}\,,\quad \lambda>0, $$
which is similar to the Berry–Esseen estimate and uses the central moments, unlike the known analogous inequalities based on the noncentral moments.
Keywords: Poisson random sum; central limit theorem; convergence rate estimate; Berry–Esseen inequality; absolute constant.
Document Type: Article
Language: Russian
Citation: V. Yu. Korolev, I. G. Shevtsova, S. Ya. Shorgin, “On the Berry–Esseen type inequalities for poisson random sums”, Inform. Primen., 5:3 (2011), 64–66
Citation in format AMSBIB
\Bibitem{KorSheSho11}
\by V.~Yu.~Korolev, I.~G.~Shevtsova, S.~Ya.~Shorgin
\paper On the Berry--Esseen type inequalities for~poisson random sums
\jour Inform. Primen.
\yr 2011
\vol 5
\issue 3
\pages 64--66
\mathnet{http://mi.mathnet.ru/ia160}
Linking options:
  • https://www.mathnet.ru/eng/ia160
  • https://www.mathnet.ru/eng/ia/v5/i3/p64
  • This publication is cited in the following 11 articles:
    1. Frolov A.N., “On Esseen Type Inequalities For Combinatorial Random Sums”, Commun. Stat.-Theory Methods, 46:12 (2017), 5932–5940  crossref  mathscinet  zmath  isi  scopus
    2. J. K. Sunklodas, “On the normal approximation under some condition for a differential equation of the characteristic function”, Lith. Math. J., 56:1 (2016), 114–126  crossref  mathscinet  isi  elib
    3. Sunklodas J.K., “on the Normal Approximation of a Binomial Random Sum”, Lith. Math. J., 54:3 (2014), 356–365  crossref  mathscinet  zmath  isi  elib
    4. L. M. Zaks, V. Yu. Korolev, “Obobschennye dispersionnye gamma-raspredeleniya kak predelnye dlya sluchainykh summ”, Inform. i ee primen., 7:1 (2013), 105–115  mathnet
    5. V. Yu. Korolev, “Generalized hyperbolic laws as limit distributions for random sums”, Theory Probab. Appl., 58:1 (2014), 63–75  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. M. E. Grigoreva, V. Yu. Korolev, “O skhodimosti raspredelenii sluchainykh summ k skoshennym eksponentsialno-stepennym zakonam”, Inform. i ee primen., 7:4 (2013), 66–74  mathnet  crossref  elib
    7. Sunklodas J.K., “$L_1$ Bounds for Asymptotic Normality of Random Sums of Independent Random Variables”, Lith. Math. J., 53:4 (2013), 438–447  crossref  mathscinet  zmath  isi  elib
    8. V. E. Bening, L. M. Zaks, V. Yu. Korolev, “Otsenki skorosti skhodimosti raspredelenii sluchainykh summ k nesimmetrichnomu raspredeleniyu Styudenta”, Sistemy i sredstva inform., 22:1 (2012), 132–141  mathnet
    9. V. E. Bening, L. M. Zaks, V. Yu. Korolev, “Otsenki skorosti skhodimosti raspredelenii sluchainykh summ k dispersionnym gamma-raspredeleniyam”, Inform. i ee primen., 6:3 (2012), 69–73  mathnet
    10. Sunklodas J.K., “On the Normal Approximation of a Sum of a Random Number of Independent Random Variables”, Lith. Math. J., 52:4 (2012), 435–443  crossref  mathscinet  zmath  isi
    11. Sunklodas J.K., “Some Estimates of Normal Approximation for the Distribution of a Sum of a Random Number of Independent Random Variables”, Lith. Math. J., 52:3 (2012), 326–333  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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