Stein's method for compound Poisson approximation: The local approach
The author considers compound Poisson approximation by Stein's method. Exploiting existence of a natural dependence structure which is appropriate for example in stationary \(m\)-mixing [\textit{M. R. Leadbetter}, \textit{G. Lindgren} and \textit{H. Rootzén}, Extremes and related properties of random sequences and processes (1983; Zbl 0518.60021)] or local dependence [\textit{A. D. Barbour}, \textit{L. H. Y. Chen} and \textit{W.-L. Loh}, Ann. Probab. 20, No. 4, 1843-1866 (1992; Zbl 0765.60015)], the author gives a bound on the total variation distance between sums of dependent 0-1 valued random variables and the Poisson distribution. An analogue of this result for compound Poisson approximation is given and later it is applied to a reliability problem involving the number of isolated vertices in the rectangular lattice on the torus.
scientific article; zbMATH DE number 731972