Lithuanian Mathematical Journal

, Volume 49, Issue 2, pp 216–221 | Cite as

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

  • J. Sunklodas


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.


central limit theorem Lp norms Poisson distribution gamma distribution 


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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsAkademijos 4, 08663 Vilnius Vilnius Gediminas Technical UniversityVilniusLithuania

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