Confidence Intervals for Quantiles and Tolerance Intervals Based on Ordered Ranked Set Samples

Abstract

Order statistics, Confidence interval, Expected width, Quantile, Percentage reduction,

Optimal sign test for quantiles in ranked set samples

“…Similar to Balakrishnan and Li (2006)'s work, we construct a confidence interval [X r:n ,X s:n ] for x p which is the pth quantile of infinite population F(x). We first have to know the probability that the random interval covers x p , PðX r:n rx p r X s:n Þ ¼ Pðx p Z X r:n ÞÀPðx p Z X s:n Þ:…”

“…Chen (2000) discussed ranked-set sample quantiles and their applications. Balakrishnan and Li (2006) considered distribution-free confidence intervals for quantiles based on ordered RSS. Ozturk and Balakrishnan (2009) proposed an exact two-sample nonparametric test for quantiles under the standard RSS.…”

Exact two-sample nonparametric test for quantile difference between two populations based on ranked set samples

“…The ranked set sample observations are independent but not identically distributed. The derivation of the pdf and cdf of the r th order statistic in this case is not trivial and are given by (see Ozturk and Deshpande 2006;Balakrishnan and Li 2006) …”

“…Chen (2000) used independent order statistics in ranked set sample to construct confidence intervals for the population quantiles. Recently, Balakrishnan and Li (2006) and Ozturk and Deshpande (2006) used order statistics of a ranked set sample to construct exact nonparametric confidence intervals for population quantiles. These authors showed that the quantile intervals based on order statistics of a ranked set sample are narrower than those constructed from independent order statistics in Chen (2000).…”

Permanents, Order Statistics, Outliers, and Robustness

“…This set of ordered observations has been referred to as ordered ranked set sample in [31,32], and has been used to develop efficient inferential procedures in this context.…”