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Asymptotic normality for the number of records from general distributions

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Raul Gouet ,
F. Javier López  and
Gerardo Sanz
Raul Gouet*
Affiliation:
Universidad de Chile
F. Javier López*
Affiliation:
Universidad de Zaragoza
Gerardo Sanz*
Affiliation:
Universidad de Zaragoza
*
∗ Postal address: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMI 2807 CNRS, Universidad de Chile, Casilla 170-3, Santiago, Chile. Email address: rgouet@dim.uchile.cl
∗∗ Postal address: Departamento de Métodos Estadí sticos and BIFI, Facultad de Ciencias, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009 Zaragoza, Spain.
∗∗ Postal address: Departamento de Métodos Estadí sticos and BIFI, Facultad de Ciencias, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009 Zaragoza, Spain.
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Abstract

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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.

Keywords

Extremesrecordscentral limit theorem

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 2 , June 2011 , pp. 422 - 436
Copyright
Copyright © Applied Probability Trust 2011 

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