ESTIMATION OF PARAMETERS OF NADARAJAH-HAGHIGHI EXTENSION OF THE EXPONENTIAL DISTRIBUTION USING PERFECT AND IMPERFECT RANKED SET SAMPLE

Abstract

The ranked set sampling (RSS) is a cost-effective method of sampling thatcan be used in a wide range of statistical problems. In this paper, the shape and thescale parameters of Nadarajah-Haghighi extension of the exponential distribution areestimated based on a simple random sample (SRS) and RSS. Three cases are considered:1) the scale parameter is known; 2) the shape parameter is known; 3) both shape andscale parameters are unknown. Observations are done when the ranking mechanism inthe ranked set sample is perfect and when it is not. Method of moments, the maximumlikelihood method, and a modification of the maximum likelihood method are used. Theobtained estimators are compared in terms of their biases and mean square errors (MSE).The results revealed that estimators based on RSS tend to show better properties (smallerbias and MSE) relative to their SRS counterparts, regardless of the quality of the ranking.