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On the rate of convergence of L p norms in the CLT for poisson and gamma random variables

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Abstract

In the paper, we present upper bounds of L p norms \( \Delta _{\mathbb{D}X,p} \) of order (\( \mathbb{D}\) X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−\( \mathbb{E}\) X)/ √\( \mathbb{D}\) X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter α > 0.

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References

  1. N. Balakrishnan and V.B. Nevzorov, A Primer on Statistical Distributions, Wiley, New Jersey, 2003.

    Book  MATH  Google Scholar 

  2. R.V. Erickson, On an L p version of the Berry–Esséen theorem for independent and m-dependent random variables, Ann. Probab., 1(3):497–503, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  3. R.V. Erickson, L 1 bounds for asymptotic normality of m-dependent sums using Stein’s technique, Ann. Probab., 2:522–529, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  4. I.A. Ibragimov and Yu.V. Linnik, Independent and Stationary Connected Variables, Nauka, Moscow, 1965 (in Russian).

    Google Scholar 

  5. M. Loève, Probability Theory. I, 4th edition, Springer-Verlag, New York, Berlin, Heidelberg, 1977.

    MATH  Google Scholar 

  6. E. Lukacs, Characteristic Functions, Nauka, Moscow, 1979 (in Russian).

    MATH  Google Scholar 

  7. Ch. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, in Proc. Math. Statist. and Probab., Vol. 2, Univ. Calif. Press, Berkeley, CA, 1972, pp. 583–602.

    Google Scholar 

  8. J. Sunklodas, On the rate of convergence of L p norms in the central limit theorem for independent random variables, Lith. Math. J., 42(3):296–307, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  9. A.N. Tikhomirov, On the rate of convergence in the central limit theorem for weakly dependent variables, Theory Probab. Appl., 25:790–809, 1980.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius Vilnius Gediminas Technical University, Saulėtekio 11, 10223, Vilnius, Lithuania

    J. Sunklodas

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  1. J. Sunklodas
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Correspondence to J. Sunklodas.

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The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09.

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Sunklodas, J. On the rate of convergence of L p norms in the CLT for poisson and gamma random variables. Lith Math J 49, 216–221 (2009). https://doi.org/10.1007/s10986-009-9039-7

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  • DOI: https://doi.org/10.1007/s10986-009-9039-7

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