Compound Poisson Approximation For Dissociated Random Variables Via Stein's Method

In the present paper we consider compound Poisson approximation by Stein’s method for dissociated random variables. We present some applications to problems in system reliability. In particular, our examples have the structure of an incomplete U-statistics. We mainly apply techniques from Barbour and Utev, who gave new bounds for the solutions of the Stein equation in compound Poisson approximation in two recent papers. DOI: https://doi.org/10.1017/S0963548399003880 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-99961 Published Version Originally published at: Eichelsbacher, Peter; Roos, Malgorzata (1999). Compound poisson approximation for dissociated random variables via Stein’s method. Combinatorics, Probability Computing, 8(4):335-346. DOI: https://doi.org/10.1017/S0963548399003880 Combinatorics, Probability and Computing http://journals.cambridge.org/CPC Additional services for Combinatorics, Probability and Computing: Email alerts: Click here Subscriptions: Click here Commercial reprints: Click here Terms of use : Click here Compound Poisson Approximation for Dissociated Random Variables via Stein's Method PETER EICHELSBACHER and MALGORZATA ROOS Combinatorics, Probability and Computing / Volume 8 / Issue 04 / July 1999, pp 335 346 DOI: null, Published online: 08 September 2000 Link to this article: http://journals.cambridge.org/abstract_S0963548399003880 How to cite this article: PETER EICHELSBACHER and MALGORZATA ROOS (1999). Compound Poisson Approximation for Dissociated Random Variables via Stein's Method. Combinatorics, Probability and Computing, 8, pp 335-346 Request Permissions : Click here Downloaded from http://journals.cambridge.org/CPC, IP address: 130.60.47.86 on 30 Oct 2014 Combinatorics, Probability and Computing (1999) 8, 335–346. Printed in the United Kingdom c © 1999 Cambridge University Press Compound Poisson Approximation for Dissociated Random Variables via Stein’s Method P E T E R E I C H E L S B A C H E R and M A L G O R Z A T A R O O S 1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany (e-mail: [email protected]) 2 Biostatistik, ISPM, Universität Zürich, Sumatrastrasse 30, CH-8006 Zürich, Switzerland (e-mail: [email protected]) Received 5 February 1998; revised 14 September 1998 In the present paper we consider compound Poisson approximation by Stein’s method for dissociated random variables. We present some applications to problems in system reliability. In particular, our examples have the structure of an incomplete U-statistics. We mainly apply techniques from Barbour and Utev, who gave new bounds for the solutions of the Stein equation in compound Poisson approximation in two recent papers.