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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 40, Fasc. 1,
pages 23 - 35
DOI: 10.37190/0208-4147.40.1.2
Published online 20.3.2020
 

LOWER BOUNDS FOR DISCRETE APPROXIMATIONS TO SUMS OF \(m\)-DEPENDENT RANDOM VARIABLES

Vydas Cekanavicius
Palaniappan Vellaisamy

Abstract: Lower bounds for the second order Poisson, compound Poisson, negative binomial and binomial approximations to the sum of 1-dependent random variables are obtained for the Kolmogorov and local metrics. The results are then applied to sums of independent indicators and runs statistics.

2010 AMS Mathematics Subject Classification: Primary 60F05; Secondary 60G50.

Keywords and phrases: Poisson approximation, signed compound Poisson measure, binomial and negative binomial approximations, one-dependent variables, local norm, Kolmogorov distance.

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