Lithuanian Mathematical Journal

, Volume 50, Issue 3, pp 323–336 | Cite as

Compound Poisson approximations for sums of 1-dependent random variables. I

  • J. Petrauskienė
  • V. Čekanavičius


We approximate two-runs statistic by various compound Poisson distributions and second-order asymptotic expansions. The accuracy of approximation is estimated in the total-variation and local metrics. For a special case, asymptotically sharp constants are calculated. Heinrich’s method is used in the proofs.


primary 60F05 secondary 60G50 


2-runs compound Poisson distribution m-dependent variables total variation norm local norm 


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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Vilnius UniversityVilniusLithuania

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