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A conditional Berry–Esseen inequality

Part of: Limit theorems Combinatorial probability Distribution theory

Published online by Cambridge University Press:  12 July 2019

Thierry Klein ,
Agnés Lagnoux  and
Pierre Petit
Thierry Klein*
Affiliation:
ENAC and Institut de Mathématiques de Toulouse (UMR CNRS 5219)
Agnés Lagnoux*
Affiliation:
Institut de Mathématiques de Toulouse (UMR CNRS 5219)
Pierre Petit*
Affiliation:
Institut de Mathématiques de Toulouse (UMR CNRS 5219)
*
*Postal address: ENAC, 7 Avenue Edouard Belin, F-31400 Toulouse, France. Email address: thierry.klein@math.univ-toulouse.fr
**Postal address: Institut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse 2, 5 Allées Antonio Machado, F-31058 Toulouse, France.
**Postal address: Institut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse 2, 5 Allées Antonio Machado, F-31058 Toulouse, France.
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Abstract

As an extension of a central limit theorem established by Svante Janson, we prove a Berry–Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.

Keywords

Berry–Esseen inequalityconditional distributioncombinatorial problemoccupancyhashing with linear probingrandom forestbranching processBose–Einstein statistics

MSC classification

Primary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory
Secondary: 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 76 - 90
Copyright
© Applied Probability Trust 2019 

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