Central limit theorems for the number of records in discrete models

被引：11

作者：

Gouet, R

López, FJ

Sanz, G

机构：

[1] Univ Chile, Dept Ingn Matemat, UMI 2807, CNRS, Santiago, Chile

[2] Univ Chile, Ctr Modelamiento Matemat, UMI 2807, CNRS, Santiago, Chile

[3] Univ Zaragoza, Fac Ciencias, Dept Metodos Estadist, E-50009 Zaragoza, Spain

来源：

ADVANCES IN APPLIED PROBABILITY | 2005年 / 37卷 / 03期

关键词：

extreme; martingale; record; central limit theorem;

D O I：

10.1239/aap/1127483747

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Consider a sequence (X-n) of independent and identically distributed random variables taking nonnegative integer values, and call X-n a record if X-n > max(X-1,..., 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.

引用

页码：781 / 800

页数：20

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