Simulation-Based Study on Extreme Ranked Set Sampling from Rician Distribution

The RSS approach is a useful method of sampling that reduces the cost and improves the representativeness of the population. It provides more efficient estimators than the competitors based on SRS. However, using RSS could be a difficult task to observe all the ranks. Thus, using only the extreme ranks eases the task and reduces the error in ranking. Samawi et al. (1996) proposed the method of Extreme Ranked Set Sampling (ERSS) to reduce errors in ranking and showed that the method gives an unbiased estimate of the population mean in the case of symmetric populations and it provides a more efficient estimator than SRS. However, the estimator of this method is biased when the distribution is skewed. Many researchers have considered ERSS, investigated several estimators, and studied their properties. In this paper, we adopt the ERSS technique when the samples are drawn from the Rician distribution. Several estimators have been studied, including arithmetic mean, geometric mean, harmonic mean, quadratic mean, median, variance, mean deviation, skewness, and kurtosis. Computer simulations were used to check the properties of these estimators and compared with the corresponding estimators using SRS. Some estimators based on ERSS are more efficient than the corresponding estimators from SRS, but some others are not.