Advances in Applied Probability

Asymptotic normality for the number of records from general distributions

Raul Gouet, F. Javier López, and Gerardo Sanz

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We provide necessary and sufficient conditions for the asymptotic normality of Nn, the number of records among the first n observations from a sequence of independent and identically distributed random variables, with general distribution F. In the case of normality we identify the centering and scaling sequences. Also, we characterize distributions for which the limit is not normal in terms of their discrete and continuous components.

Article information

Adv. in Appl. Probab., Volume 43, Number 2 (2011), 422-436.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F05: Central limit and other weak theorems

Extremes records central limit theorem


Gouet, Raul; López, F. Javier; Sanz, Gerardo. Asymptotic normality for the number of records from general distributions. Adv. in Appl. Probab. 43 (2011), no. 2, 422--436.

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