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Poisson approximation for a sum of dependent indicators: an alternative approach

Part of:Limit theorems

Published online by Cambridge University Press:  01 July 2016

N. Papadatos and
V. Papathanasiou
N. Papadatos*
Affiliation:
University of Athens
V. Papathanasiou*
Affiliation:
University of Athens
*
∗ Postal address: Section of Statistics and Operational Research, Department of Mathematics, University of Athens, Panepistemiopolis, 157 84 Athens, Greece.
∗ Postal address: Section of Statistics and Operational Research, Department of Mathematics, University of Athens, Panepistemiopolis, 157 84 Athens, Greece.
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Abstract

The random variables X 1, X 2, …, X n are said to be totally negatively dependent (TND) if and only if the random variables X i and ∑j≠i X j are negatively quadrant dependent for all i. Our main result provides, for TND 0-1 indicators X 1, x 2, …, X n with P[X i = 1] = p i = 1 - P[X i = 0], an upper bound for the total variation distance between ∑n i=1 X i and a Poisson random variable with mean λ ≥ ∑n i=1 p i . An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

Keywords

Totally negatively dependent indicatorChen-Stein equationnegatively related indicatorPoisson approximationtotal variation distancebirthday problemmonotone coupling

MSC classification

Primary:60F05: Central limit and other weak theorems

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 3 , September 2002, pp. 609 - 625
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Research partially supported by the research foundation of the University of Athens.

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