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Activity Number: 369
Type: Topic Contributed
Date/Time: Wednesday, August 9, 2006 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #306516
Title: Confidence Intervals for Quantiles Based on Ranked Set Samples
Author(s): Tao Li*+ and Narayanaswamy Balakrishnan
Companies: St. Francis Xavier University and McMaster University
Address: P.O. Box 5000, Antigonish, NS, B2G 1V5, Canada
Keywords: ordered statistics ; ranked set sample ; confidence interval ; expected width ; percentage reduction ; ordered ranked set sample
Abstract:

Confidence intervals for quantiles and tolerance intervals based on ordered ranked set samples (ORSS) will be discussed. 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. Then, confidence intervals for quantiles based on ORSS are derived and their properties discussed. We compare, with approximate confidence, intervals for quantiles and show that these approximate confidence intervals are not 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 the confidence interval based on ORSS becomes considerably narrower than the one based on usual order statistics when size n becomes large.

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