Discrete approximations for sums of m-dependent random variables

V. Čekanavičius; P. Vellaisamy

Discrete approximations for sums of m-dependent random variables

Statistics Theory 2015-11-05 v3 Statistics Theory

Authors: V. Čekanavičius , P. Vellaisamy

Abstract

Sums of of 1-dependent integer-valued random variables are approximated by compound Poisson, negative binomial and Binomial distributions and signed compound Poisson measures. Estimates are obtained for total variation and local metrics. The results are then applied to statistics of $m$ -dependent $(k_1,k_2)$ events and 2-runs. Heinrich's method and smoothing properties of convolutions are used for the proofs.

Keywords

probability theory stein's method probability distribution

Cite

@article{arxiv.1301.7196,
  title  = {Discrete approximations for sums of m-dependent random variables},
  author = {V. Čekanavičius and P. Vellaisamy},
  journal= {arXiv preprint arXiv:1301.7196},
  year   = {2015}
}

Comments

Revised and shortened version

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