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Central limit theorems for the number of records in discrete models

Part of: Stochastic processes

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 y Centro de Modelamiento Matemático, Universidad de Chile, UMI-CNRS-2807, Casilla 170-3, Correo 3, Santiago, Chile. Email address: [email protected]
∗∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
∗∗ Postal address: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
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Abstract

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Consider a sequence (Xn) of independent and identically distributed random variables taking nonnegative integer values, and call Xn a record if Xn> max{X1,…,Xn−1}. By means of martingale arguments it is shown that the counting process of records among the first n observations, suitably centered and scaled, is asymptotically normally distributed.

Keywords

Extrememartingalerecordcentral limit theorem

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G42: Martingales with discrete parameter
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 3 , September 2005 , pp. 781 - 800
Copyright
Copyright © Applied Probability Trust 2005 

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