On large deviations for sums of discrete m-dependent random variables
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The ratio P(S_n=x)/P(Z_n=x) is investigated for three cases: (a) when S_n is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and Z_n is Poisson rv; (b) when S_n is a statistic of 2-runs and Z_n is negative binomial rv; and (c) when S_n is statistic of N(1,1)-events and Z_n is a binomial r.v. We also consider the approximation of P(S_n≥ x) by Poisson distribution with parameter depending on x.
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