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PARAMETRIC RANKED SET SAMPLING

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LYNNE STOKES

*Department of Management Science and Information Systems,*

University of Texas at Austin, CBA 5.202, Austin, TX
78712-1175,
U.S.A.
(Received March 15, 1994; revised December 6, 1994)

**Abstract.**
Ranked set sampling was introduced by
McIntyre (1952, *Australian Journal of Agricultural
Research*, **3**, 385-390) as a cost-effective method of
selecting data if observations are much more cheaply ranked than
measured. He proposed its use for estimating the population mean
when the distribution of the data was unknown. In this paper, we
examine the advantage, if any, that this method of sampling has
if the distribution is known, for a specific family of
distributions. Specifically, we consider estimation of *mu* and
*sigma* for the family of random variables with cdf's of the
form *F*(*x*-*mu*/*sigma*). We find that the ranked set sample
does provide more information about both *mu* and *sigma* than
a random sample of the same number of observations. We examine
both maximum likelihood and best linear unbiased estimation of
*mu* and *sigma*, as well as methods for modifying the ranked
set sampling procedure to provide even better estimation.

*Key words and phrases*:
Order statistic, ranked set
sample, maximum likelihood estimator, best linear unbiased
estimator.

**Source**
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