ESTIMATION OF PARAMETERS IN A TWO-PARAMETER EXPONENTIAL DISTRIBUTION USING RANKED SET SAMPLE

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

1Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong 2Department 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.