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New insights on goodness-of-fit tests for ranked set samples

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Abstract

Ranked set sampling (RSS) utilizes auxiliary information on the variable of interest so as to assist the experimenter in acquiring an informative sample from the population. The resulting sample has a stratified structure, and often improves statistical inference with respect to the simple random sample of comparable size. In RSS literature, there are some goodness-of-fit tests based on the empirical estimators of the in-stratum cumulative distribution functions (CDFs). Motivated by the fact that the in-stratum CDFs in RSS can be expressed as functions of the population CDF, some new tests are developed and their asymptotic properties are explored. An extensive simulation study is performed to evaluate properties of different testing procedures when the parent distribution is normal. It turns out that the proposed tests can be considerably more powerful than their contenders in many situations. An application in the context of fishery is also provided.

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  1. https://cran.r-project.org/web/packages/FSAdata/index.html.

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Acknowledgements

The authors wish to thank the reviewers for their helpful comments that have improved this article. Ehsan Zamanzade’s research was carried out in IPM Isfahan branch and was in part supported by a grant from IPM, Iran (No. 1400620422).

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Authors and Affiliations

  1. Department of Statistics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran

    M. Mahdizadeh

  2. Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, 81746-73441, Isfahan, Iran

    Ehsan Zamanzade

  3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Ehsan Zamanzade

Authors
  1. M. Mahdizadeh
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  2. Ehsan Zamanzade
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Appendix

Appendix

Table 1 Estimated powers of level-0.05 tests for the simple hypothesis that the distribution is standard normal when \(N=10\) and \(\lambda =1\)
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Table 2 Estimated powers of level-0.05 tests for the simple hypothesis that the distribution is standard normal when \(N=10\) and \(\lambda =1\)
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Table 3 Estimated powers of level-0.05 tests for the simple hypothesis that the distribution is standard normal when \(N=20\) and \(\lambda =1\)
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Table 4 Estimated powers of level-0.05 tests for the simple hypothesis that the distribution is standard normal when \(N=20\) and \(\lambda =1\)
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Table 5 Estimated powers of level-0.05 tests for the composite hypothesis of normality when \(N=10\) and \(\lambda =1\)
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Table 6 Estimated powers of level-0.05 tests for the composite hypothesis of normality when \(N=10\) and \(\lambda =1\)
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Table 7 Estimated powers of level-0.05 tests for the composite hypothesis of normality when \(N=20\) and \(\lambda =1\)
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Table 8 Estimated powers of level-0.05 tests for the composite hypothesis of normality when \(N=20\) and \(\lambda =1\)
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Table 9 A ranked set sample of size \(N=20\) drawn from AnchovetaChile data using \(m=5\)
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Table 10 Values of the test statistics computed from the sample in Table 9
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Mahdizadeh, M., Zamanzade, E. New insights on goodness-of-fit tests for ranked set samples. Stat Papers 63, 1777–1799 (2022). https://doi.org/10.1007/s00362-021-01284-7

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  • DOI: https://doi.org/10.1007/s00362-021-01284-7

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