Discrete approximations for sums of m-dependent random variables

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.

Revised and shortened version

References in corpus (1)

• Compound Poisson and signed compound Poisson approximations to the Markov binomial law

Cited by in corpus (2)

• Smoothing effect of Compound Poisson approximation to distribution of weighted sums
• On large deviations for sums of discrete m-dependent random variables