Abstract
This paper describes the modified maximum likelihood estimator (MMLE) of location and scale parameters based on selected ranked set sampling (SRSS) for normal, uniform and two-parameter exponential distributions. For these distributions, the MMLE of location and scale parameters for SRSS data were compared with the estimators of location and scale parameters for simple random sample (SRS) and ranked set sample (RSS). The MMLE based on SRSS data were found to be advantageous as compared to SRS and RSS estimators for the same number of measurements. The SRSS method with errors in ranking was also described. The minimum correlation between the actual and erroneous ranking was required for MMLE of SRSS to achieve better precision than usual SRS and RSS estimators. When the wrong assumption about the underlying distribution was present, the MMLE of the population mean based on SRSS was better than the RSS estimator ofthe population mean for all the cases considered.
Highlights
Sampling is the process of selecting some representative part of a population to estimate unknown characteristics by observing the selected part of the population
When the number of measurements was small and the cost of measurements was high, instead of simple random sample (SRS) and Ranked set sampling (RSS) a precise estimator could be obtained by using selected ranked set sampling (SRSS) method
We compared maximum likelihood estimator (MMLE) for SRSS with SRS and RSS estimators based on the same numbers of measurements
Summary
Sampling is the process of selecting some representative part of a population to estimate unknown characteristics by observing the selected part of the population. Zheng and Al-Saleh (2002) showed that, the MMLE for the location parameter was always more efficient than the MLE using SRS and for the scale parameter, the MMLE was at least as efficient as the MLE using SRS, when the same sample size was used They found that in case of perfect judgement ranking, MMLE was relatively efficient than MLE based on RSS. The MMLE of the location and scale parameters based on SRSS data were studied These estimators were compared with usual estimators based on SRS and RSS data for normal, uniform and two-parameter exponential distributions. Present sampling method seems to be quite appealing because SRSS estimators are expected to be more precise than those obtained by SRS and RSS with the same number of measurements when the underlying distribution is known (Hossain and Muttlak, 2001)
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