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Activity Number: 617 - Recent Developments on Order-Related Designs and Inferences
Type: Topic Contributed
Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #322739
Title: Ranked Set Sampling Estimators of Discrete Distribution Parameters
Author(s): Bingchen Liu* and Lynne Stokes
Companies: Educational Testing Service and Southern Methodist University
Keywords: Judgment ranking ; Order statistics ; Discrete distribution ; Ties

This paper examines ranked set sampling (RSS) for discrete random variables. We examined the performance of the usual RSS mean estimator for discrete random variables where actual ties may be present in the sample. We found that the discreteness of the population (measured by the expected number of ties in the sample) lead to less advantage for RSS over simple random sample (SRS). We propose an estimator which uses the tie information in the sample and compared it to an estimator proposed by Frey (2012). We provided a justification of Frey's estimator, and showed that it is justifiable when the ranked set sample is balanced, and there are no errors in the assessment of ties. Both estimators incorporate the tie information, and have higher efficiency than the usual RSS estimator of mean.

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