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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Abstract

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

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

Dates
First available in Project Euclid: 21 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.aap/1308662486

Mathematical Reviews number (MathSciNet)
MR2848383

Zentralblatt MATH identifier
1234.60058

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

Keywords
Extremes records central limit theorem

Citation

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. https://projecteuclid.org/euclid.aap/1308662486


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References

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