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ESTIMATION OF PARAMETERS IN A TWO-PARAMETER

EXPONENTIAL DISTRIBUTION USING RANKED SET SAMPLE

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KIN LAM^{1}, BIMAL K. SINHA^{2} AND ZHONG WU^{2}

^{1} *Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong*

^{2} *Department of Mathematics and Statistics, University of Maryland Baltimore County,*

Baltimore, MD 21228-5398, U.S.A.
(Received June 30, 1993; revised April 28, 1994)

**Abstract.**
In situations where the experimental or
sampling units in a study can be easily ranked than quantified,
McIntyre (1952, *Aust. J. Agric. Res.*, **3**,
385-390) proposed that the mean of *n* units based on a
*ranked set sample* (*RSS*) be used to estimate the
population mean, and observed that it provides an unbiased
estimator with a smaller variance compared to a simple random
sample (*SRS*) of the same size *n*. McIntyre's concept of
*RSS* is essentially nonparametric in nature in that the
underlying population distribution is assumed to be completely
unknown. In this paper we further explore the concept of
*RSS* when the population is partially known and the parameter of
interest is not necessarily the mean. To be specific, we address the
problem of estimation of the parameters of a two-parameter
exponential distribution. It turns out that the use of *RSS*
and its suitable modifications results in much improved estimators
compared to the use of a *SRS*.

*Key words and phrases*:
Best linear unbiased estimator,
exponential distribution, order statistics, ranked set sample,
uniformly minimum variance unbiased estimator.

**Source**
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