On the estimation of population mean based on modified ranked set sampling

Ranked set sampling (RSS) is an efficient and advantageous method for estimating the population mean when the measurement of an observation is time consuming and/or expensive. RSS procedure is based upon ranking the units without the actual measurement of the variable of interest. This method come into prominence recently due to the efficiency and cost effectiveness. RSS method has been modified by various researchers. One of them is Balanced Groups RSS which takes into account measurements of the lowest, median and the largest ranked units of the sets. It is revealed that Balanced Groups RSS is more efficient than commonly used Simple Random Sampling (SRS) and it gives unbiased results when the underlying distribution is symmetric. In this study, we propose an improvement of the sampling procedure of Balanced Groups RSS which is called Adjusted-Balanced Groups RSS for even and odd set sizes in decreasing the ranking error and the cost of the method. Adjusted-Balanced Groups RSS offers a more flexible sampling plan ensuring the independence of the set and sample sizes. Also, we propose a weighted estimator with a weight formula to obtain an efficient estimation of the population mean when the underlying distribution is skewed. A Monte Carlo simulation study is conducted for comparing the performance of the mean estimators according to mean squared errors and sampling costs for the methods of Adjusted-Balanced Groups RSS, Balanced Groups RSS, Median RSS, Percentile RSS and Extreme RSS in various type of distributions. Moreover, we compare the efficiencies of the proposed weighted estimator in Balanced Groups RSS and the classical estimator for the population mean in different type of asymmetric probability distributions with different set and sample sizes.