MULTISTAGE BALANCED GROUPS RANKED SET SAMPLES FOR ESTIMATING THE POPULATION MEDIAN

Amer Ibrahim Al-Omari; Kamarulzaman Ibrahim; Abdul Aziz Jemain; Said Ali Al-Hadhrami

doi:https://doi.org/10.59170/stattrans-2009-017

MULTISTAGE BALANCED GROUPS RANKED SET SAMPLES FOR ESTIMATING THE POPULATION MEDIAN

Amer Ibrahim Al-Omari Department of Mathematics, Faculty of Science and Nursing, Jerash Private University, Jordan. , Kamarulzaman Ibrahim School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia. , Abdul Aziz Jemain School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia. , Said Ali Al-Hadhrami Department of Mathematics, College of Applied Sciences, Nizwa, Oman. Statistics in Transition new series, vol. 10, 2009, 2, pages: 223-233 Published online: 1 October 2009 https://doi.org/10.59170/stattrans-2009-017

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ABSTRACT

A multistage balanced groups ranked set samples (MBGRSS) method and its properties for estimating the population median is considered. The suggested estimator is compared to those obtained based on simple random sampling (SRS) and the ranked set sampling (RSS) methods. The MBGRSS estimator of the population median is found to be unbiased if the underlying distribution is symmetric and has a small bias if the underlying distribution is asymmetric, the bias is decreasing in r (r is the number of stage). It is found that, MBGRSS is as efficient as RSS when m = 3 and r = 1 , and it is more efficient than RSS for r > 1 . However, the efficiency of MBGRSS is increasing in r for specific value of the sample size whether the underlying distribution is symmetric or asymmetric. Real data is used to illustrate the method.

KEYWORDS

Ranked set sampling; simple random sampling; balanced groups ranked set samples, symmetric distribution; asymmetric distribution.

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