ON RECORD VALUES AND THE EXPONENT OF A DISTRIBUTION WITH REGULARLY VARYING UPPER TAIL

被引：11
作者：
BERRED, M [1 ]
机构：
[1] UNIV PARIS 06,F-75005 PARIS,FRANCE
来源：
JOURNAL OF APPLIED PROBABILITY | 1992年 / 29卷 / 03期
关键词：
RECORDS; EXTREME VALUES; REGULAR VARIATION; PARAMETRIC ESTIMATION; TAIL ESTIMATION;
D O I：
10.2307/3214894
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：
Let {X(n), n greater-than-or-equal-to 1) be an i.i.d. sequence of positive random variables with a continuous distribution function having a regularly varying upper tail. Denote by {X(n), n greater-than-or-equal-to 1) the corresponding sequence of record values. We introduce two statistics based on the sequence of successive record values and investigate their asymptotic behaviour. We also give some numerical results.
引用
收藏
页码：575 / 586
页数：12
相关论文
共 19 条
[1]  
Bingham N.H., 1987, REGULAR VARIATION
[2]   KERNEL ESTIMATES OF THE TAIL INDEX OF A DISTRIBUTION [J].
CSORGO, S ;
DEHEUVELS, P ;
MASON, D .
ANNALS OF STATISTICS, 1985, 13 (03) :1050-1077
[3]  
DEHAAN L, 1980, J ROY STAT SOC B MET, V42, P83
[4]  
DEHEUVELS P, 1990, B SCI MATH, V114, P61
[5]  
DEHEUVELS P, 1988, B SCI MATH, V112, P211
[6]   ALMOST SURE CONVERGENCE OF THE HILL ESTIMATOR [J].
DEHEUVELS, P ;
HAEUSLER, E ;
MASON, DM .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 104 :371-381
[7]   SLOW VARIATION WITH REMAINDER - THEORY AND APPLICATIONS [J].
GOLDIE, CM ;
SMITH, RL .
QUARTERLY JOURNAL OF MATHEMATICS, 1987, 38 (149) :45-71
[8]   ON ASYMPTOTIC NORMALITY OF HILL ESTIMATOR FOR THE EXPONENT OF REGULAR VARIATION [J].
HAEUSLER, E ;
TEUGELS, JL .
ANNALS OF STATISTICS, 1985, 13 (02) :743-756
[9]  
HALL P, 1982, J ROY STAT SOC B MET, V44, P37
[10]   ON THE LAW OF LARGE NUMBERS [J].
HANSON, DL ;
RUSSO, RP .
ANNALS OF PROBABILITY, 1981, 9 (03) :513-519
12