JSM 2004 - Toronto

Abstract #300419

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Activity Number: 311
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #300419
Title: Estimating the Parameters of the Normal Using Median and Extreme Ranked-set Samples
Author(s): Hassen A. Muttlak*+
Companies: King Fahd University of Petroleum and Minerals
Address: P.O. Box 1676, Dhahran, 31261, Sauda Arabia
Keywords: simple random sample ; ranked-set sample ; maximum likelihood estimate ; linear unbiased estimate ; Fisher information ; relative precision
Abstract:

In this paper, we propose maximum likelihood estimators (MLEs) as well as linear unbiased estimators (LUEs) of the parameters of the normal distribution, using median ranked-set sampling (MRSS) and extreme ranked set sampling (ERSS). MRSS and ERSS are modifications of ranked set sampling (RSS), which are more practicable and less prone to problems resulting from erroneous ranking. The MLEs of the mean under MRSS are shown to dominate all other estimators, while the mle of the normal standard deviation under ERSS is the most efficient. A similar trend is observed in the LUEs. A modification of ERSS, namely, partial extreme ranked-set sampling (PERSS), is proposed for odd set sizes to generate even-sized samples. The LUE of the normal standard deviation under this modification is shown to be the most efficient of all the LUEs of the same parameter. Among the LUEs considered, the PERSS LUEs are the most efficient when the sample size per cycle is two.

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