Open AccessEstimation of parameters of Nadarajah-Haghighi extension of the exponential distribution using perfect and imperfect ranked set sample
Author(s) -
Marija Minic
Publication year - 2020
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor190415027m
Subject(s) - estimator , mathematics , rss , statistics , ranking (information retrieval) , extension (predicate logic) , mean squared error , sample size determination , scale (ratio) , scale parameter , sample (material) , exponential distribution , range (aeronautics) , exponential function , computer science , artificial intelligence , physics , chemistry , materials science , chromatography , quantum mechanics , composite material , programming language , operating system , mathematical analysis
The ranked set sampling (RSS) is a cost-effective method of sampling that can be used in a wide range of statistical problems. In this paper, the shape and the scale parameters of Nadarajah-Haghighi extension of the exponential distribution are estimated 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 and scale parameters are unknown. Observations are done when the ranking mechanism in the ranked set sample is perfect and when it is not. Method of moments, the maximum likelihood method, and a modification of the maximum likelihood method are used. The obtained 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 (smaller bias and MSE) relative to their SRS counterparts, regardless of the quality of the ranking.