Discrete approximations for sums of m-dependent random variables

2013/01/30 by V. Čekanavičius, P. Vellaisamy, Čekanavičius, V. +1
Decision Sciences · Mathematics · #60F05 #FOS: Mathematics #Mathematical Approximation and Integration #Probability and Risk Models #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1301.7196

openalex publication_date 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (k₁,k₂) events and 2-runs. Heinrich's method and smoothing properties of convolutions are used for the proofs.

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