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Teor. Veroyatnost. i Primenen., 2007, Volume 52, Issue 1, Pages 186–190 (Mi tvp14)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Estimates for moduli of smoothness of distribution functions

J. A. Adell, A. Lekuona

University of Zaragoza

Abstract: We give upper bounds for the usual moduli of smoothness of a distribution function $F$ in terms of its characteristic function $\varphi$. In particular, we complete some known estimates of the concentration function of $F$. Our approach uses a new version of the classical Berry–Esseen smoothing inequality.

Keywords: modulus of smoothness, concentration function, characteristic function, smoothing inequality.

DOI: https://doi.org/10.4213/tvp14

Full text: PDF file (587 kB)
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English version:
Theory of Probability and its Applications, 2008, 52:1, 148–152

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Received: 22.11.2004
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Citation: J. A. Adell, A. Lekuona, “Estimates for moduli of smoothness of distribution functions”, Teor. Veroyatnost. i Primenen., 52:1 (2007), 186–190; Theory Probab. Appl., 52:1 (2008), 148–152

Citation in format AMSBIB
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\pages 186--190
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\transl
\jour Theory Probab. Appl.
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\vol 52
\issue 1
\pages 148--152
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  • https://doi.org/10.4213/tvp14
  • http://mi.mathnet.ru/eng/tvp/v52/i1/p186

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Adell J.A., Lekuona A., “Berry–Esseen bounds for standardized subordinators via moduli of smoothness”, J. Theoret. Probab., 20:2 (2007), 221–235  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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