Geodesic
Estimation of Parameters of Nadarajah-Haghighi Extension of the Exponential Distribution Using Perfect and Imperfect Ranked Set Sample
Yugoslav journal of operations research, Tome 30 (2020) no. 2, p. 177 .

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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.
Classification : 62F10, 62F07
Keywords: Nadarajah-Haghighi Extension of the Exponential Distribution, Ranked set Sampling, Simple Random Sampling, Imperfect Ranking. 
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     author = {Marija Mini\'c},
     title = {Estimation of {Parameters} of {Nadarajah-Haghighi} {Extension} of the {Exponential} {Distribution} {Using} {Perfect} and {Imperfect} {Ranked} {Set} {Sample}},
     journal = {Yugoslav journal of operations research},
     pages = {177 },
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2020_30_2_a3/}
}
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Marija Minić. Estimation of Parameters of Nadarajah-Haghighi Extension of the Exponential Distribution Using Perfect and Imperfect Ranked Set Sample. Yugoslav journal of operations research, Tome 30 (2020) no. 2, p. 177 . http://geodesic.mathdoc.fr/item/YJOR_2020_30_2_a3/