Poisson approximation in a Poisson limit theorem inspired by coupon collecting
Anna Pósfai
Source: J. Appl. Probab.
Volume 46, Number 2
(2009), 585-592.
Abstract
In this paper we refine a Poisson limit theorem of Gnedenko and
Kolmogorov (1954): we determine the error order of a
Poisson approximation for sums of asymptotically negligible integer-valued random variables that converge in
distribution to the Poisson law. As an application of our results, we investigate the case of the coupon collector's
problem when the distribution of the collector's waiting time is asymptotically Poisson.
Primary Subjects: 60F05, 62E17, 62E20
Keywords: Poisson limit theorem; Poisson approximation; total variation distance; coupon collecting
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription.
Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676108
Digital Object Identifier: doi:10.1239/jap/1245676108
References
Barbour, A. D. and Hall, P. (1984). On the rate of Poisson convergence. Math. Proc. Camb. Phil. Soc. 95, 473--480.
Mathematical Reviews (MathSciNet):
MR755837
Barbour, A. D., Holst, L. and Janson, S. (1992). Poisson Approximation (Oxford Stud. Prob. 2). Clarendon Press, New York.
Baum, L. E. and Billingsley, P. (1965). Asymptotic distributions for the coupon collector's problem. Ann. Math. Statist. 36, 1835--1839.
Mathematical Reviews (MathSciNet):
MR182039
Gnedenko, B. V. and Kolmogorov, A. N. (1954). Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Cambridge, MA.
Mathematical Reviews (MathSciNet):
MR62975
Le Cam, L. (1960). An approximation theorem for the Poisson binomial distribution. Pacific J. Math. 10, 1181--1197.
Mathematical Reviews (MathSciNet):
MR142174
Lindvall, T. (1992). Lectures on the Coupling Method. John Wiley, New York.
Pósfai, A. (2007). Rates of convergence for normal approximation in incomplete coupon collection. Acta. Sci. Math. 73, 333--348.
Pósfai, A. (2009). A supplement to the paper Poisson approximation in a Poisson limit theorem inspired by coupon collecting. Preprint. Available at http://arxiv.org/abs/0904.4924.
Pósfai, A. and Csörgő, S. (2008). Asymptotic approximations for coupon collectors. Studia Sci. Math. Hung. 46, 61--96.
