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Abstract

In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.

Keywords

Permutation test Extreme ranked set sampling Power level Type I error probability

Article Details

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Author Biographies

Monjed H. Samuh, Associate Professor of Statistics, Applied Mathematics and Physics Department, Palestine Polytechnic University Hebron - PALESTINE

Dr. Monjed H. Samuh is an associate professor of Statistics at the department of Applied Mathematics and Physics, Palestine Polytechnic University, Palestine. He obtained his PhD in Statistics from Padua University, Italy in 2012. He published about 20 research papers in peer-reviewed journals and attended 14 international conferences. His research interests include Permutation Testing, Sampling Theory, and Distribution Theory. Dr. Samuh is currently the head of Applied Mathematics and Physics Department at Palestine Polytechnic University.

Ridwan A. Sanusi, Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China

Ridwan Adeyemi SANUSI received his Ph.D. from the department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong. During his PhD program, he was a visiting scholar at the department of Industrial Engineering, Tsinghua University, Beijing, China. Prior to these, he received his M.Sc. in Applied Statistics from King Fahd University of Petroleum & Minerals, Saudi Arabia, and B.Sc. in Statistics (First Class Honors) from University of Ibadan, Nigeria. His research areas are applied statistics, industrial engineering, nonparametric statistics, statistical process control, among others. He has published in top journals, presented in international conferences, and has few international awards to his name. 
How to Cite
Samuh, M. H., & Sanusi, R. A. (2020). Permutation Tests for Two-sample Location Problem Under Extreme Ranked Set Sampling. Pakistan Journal of Statistics and Operation Research, 16(2), 387-408. https://doi.org/10.18187/pjsor.v16i2.2746

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