DEPENDENCE BETWEEN ORDER STATISTICS IN SAMPLES
FROM FINITE POPULATION AND ITS APPLICATION
TO RANKED SET SAMPLING

KOITI TAKAHASI1 AND MASAO FUTATSUYA2

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

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

(Received June 4, 1996; revised February 10, 1997)

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 X(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.

Key words and phrases:    Ranked set sampling, finite population, order statistics, dependence.

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