ON OUTSTANDING VALUES IN A SEQUENCE OF RANDOM VARIABLES

被引：73

作者：

TATA, MN

机构：

[1] Department of Statistics and Probability, Michigan State University, East Lansing, 48823, Mich., Wells Hall

来源：

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE | 1969年 / 12卷 / 01期

关键词：

D O I：

10.1007/BF00538520

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：

A sequence {Xn} of independent and identically distributed (i.i.d.) random variables is considered. Outstanding values in the sequence are those that strictly exceed values preceding them. Let Ln be the index of the n-th outstanding value. Limit theorems are given for the sequences {Mathematical expression} and {Ln} and {δn} where δn=Ln-Ln-1. A characterization of the exponential distribution in terms of the sequence {Mathematical expression} is also given. © 1969 Springer-Verlag.

引用

页码：9 / &

共 11 条

[1] BARNDORFF-NIELSEN O., 1964, ACTA MATH ACAD SCI H, V15, P399
[2] BERMAN SM, 1964, ANN MATH STATISTICS, V35, P391
[3] FOSTER FG, 1954, J ROY STAT SOC B, V16, P1
[4] The limited distribution of the maximum term of a random series
Gnedenko, B
[J]. ANNALS OF MATHEMATICS, 1943, 44 : 423 - 453
[5] KARLIN S, 1966, FIRST COURSE STOCHAS, P487
[6] LEHMANN EL, 1959, TESTING STATISTICAL, P74
[7] LOEVE M, 1963, PROBABILITY THEORY, P184
[8] NEUTS MF, TO BE PUBLISHED
[9] RENYI A, 1962, AUG COLL COMB METH P
[10] WIDDER DV, 1966, LAPLACE TRANSFORM, P182

← 1 2 →