On large deviations for sums of discrete m-dependent random variables

2019/01/10 by Čekanavičius, Vydas, Vellaisamy, Palaniappan
#60F10 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1901.03348

Abstract

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\geqslant x) by Poisson distribution with parameter depending on x.

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