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On the stability of characterizations by an identical distribution property

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Abstract

Let X 1, X 2, … , X n be i.i.d. random variables with common distribution F, and let b 1, b 2, … , b n be real coefficients such that ∑ b j 2 = 1. We prove that F is close to the normal distribution in the Lévy metric whenever the distribution of the linear statistic ∑ b j X j is close to F.

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Authors and Affiliations

  1. Vilnius Pedagogical University, Studentu 39, LT-08106, Vilnius, Lithuania

    R. Yanushkevichius & O. Yanushkevichiene

  2. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania

    O. Yanushkevichiene

Authors
  1. R. Yanushkevichius
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  2. O. Yanushkevichiene
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Correspondence to R. Yanushkevichius.

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Yanushkevichius, R., Yanushkevichiene, O. On the stability of characterizations by an identical distribution property. Lith Math J 50, 489–494 (2010). https://doi.org/10.1007/s10986-010-9101-5

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  • DOI: https://doi.org/10.1007/s10986-010-9101-5

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