Confidence intervals for quantiles and tolerance intervals based on ordered ranked set samples

被引：40

作者：

Balakrishnan, N.

Li, T. ^{[1
]}

机构：

[1] St Francis Xavier Univ, Dept Math Stat & Comp Sci, Antigonish, NS B2G 2W5, Canada

[2] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2006年 / 58卷 / 04期

关键词：

order statistics; confidence interval; expected width; quantile; percentage reduction;

D O I：

10.1007/s10463-006-0035-y

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：

Confidence intervals for quantiles and tolerance intervals based on ordered ranked set samples (ORSS) are discussed in this paper. For this purpose, we first derive the cdf of ORSS and the joint pdf of any two ORSS. In addition, we obtain the pdf and cdf of the difference of two ORSS, viz. X-s: N(ORSS) - X-r:N(ORSS) 1 <= r < s <= N. Then, confidence intervals for quantiles based on ORSS are derived and their properties are discussed. We compare with approximate confidence intervals for quantiles given by Chen ( Journal of Statistical Planning and Inference, 83, 125 - 135; 2000), and show that these approximate confidence intervals are not very accurate. However, when the number of cycles in the RSS increases, these approximate confidence intervals become accurate even for small sample sizes. We also compare with intervals based on usual order statistics and find that the confidence interval based on ORSS becomes considerably narrower than the one based on usual order statistics when n becomes large. By using the cdf of X-s: N(ORSS) - X-r:N(ORSS) we then obtain tolerance intervals, discuss their properties, and present some tables for two-sided tolerance intervals.

引用

页码：757 / 777

页数：21

共 19 条

[1]

Arnold B. C., 1998, A First Course in Order Statistics

[2] RECURRENCE RELATIONS AMONG MOMENTS OF ORDER-STATISTICS FROM 2 RELATED SETS OF INDEPENDENT AND NON-IDENTICALLY DISTRIBUTED RANDOM-VARIABLES [J].