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Dependence Between Order Statistics in Samples from Finite Population and its Application to Ranked Set Sampling

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Abstract

Let X1, X2,..., Xm, Y1, Y2,..., Yn be a simple random sample without replacement from a finite population and let X(1) ≤ X(2) ≤...≤ X(m) and Y(1) ≤ Y(2) ≤...≤ Y(n) be the order statistics of X1, X2,..., Xm and Y1, Y2,..., Yn, respectively. It is shown that the joint distribution of X(i) and X(j) is positively likelihood ratio dependent and Y(j) is negatively regression dependent on X(i). Using these results, it is shown that when samples are drawn without replacement from a finite population, the relative precision of the ranked set sampling estimator of the population mean, relative to the simple random sample estimator with the same number of units quantified, is bounded below by 1.

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Authors and Affiliations

  1. Department of Basic Science, School of Science and Engineering, Ishinomaki Senshu University, Ishinomaki, 986-80, Japan

    Koiti Takahasi

  2. Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki University, Hirosaki, 036, Japan

    Masao Futatsuya

Authors
  1. Koiti Takahasi
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  2. Masao Futatsuya
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Takahasi, K., Futatsuya, M. Dependence Between Order Statistics in Samples from Finite Population and its Application to Ranked Set Sampling. Annals of the Institute of Statistical Mathematics 50, 49–70 (1998). https://doi.org/10.1023/A:1003497213823

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  • DOI: https://doi.org/10.1023/A:1003497213823

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