A conditional Berry-Esseen inequality

Thierry Klein 1 Agnès Lagnoux 2 P Petit 2
1 ENAC - Ecole Nationale de l'Aviation Civile
2 IMT - Institut de Mathématiques de Toulouse UMR5219
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 inequality random forests combinatorial problems branching processes conditional distribution 62E20 occupancy hashing with linear probing Bose-Einstein statistics 1991 Mathematics Subject Classification: 60F05 60C05
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Thierry Klein, Agnès Lagnoux, P Petit. A conditional Berry-Esseen inequality. Journal of Applied Probability, Applied Probability Trust, 2019, 56 (1), pp 76-90. ⟨10.1017/jpr.2019.7⟩. ⟨hal-01801795⟩

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