Estimation of the mean of the exponential distribution using moving extremes ranked set sampling
Moving Extremes Ranked Set Sampling (MERSS) is a useful modification of Ranked Set Sampling (RSS). Unlike RSS, MERSS allows for an increase of set size without introducing too much ranking error. The method is considered parametrically under exponential distribution. Maximum likelihood estimator (MLE), and a modified MLE are considered and their properties are studied. The method is studied under both perfect and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE using the usual simple random sampling (SRS).
KeywordsRanked Set Sampling Moving Extremes Ranked Set Sampling Error in Ranking Maximum Likelihood Estimator Modified Maximum Likelihood Estimator
Al-Saleh, M. Fraiwan and Al-Omary
. (2002). Multistage ranked set sampling. Journal of Statistical Planning and Inferences 102
, 31–44.Google Scholar
Al-Odat, M.T. and Al-Saleh, M. Fraiwan
(2001). A variation of ranked set sampling. Journal of Applied Statistical Science 10
, 137–146.MathSciNetGoogle Scholar
Al-Saleh, M. Fraiwan and Al-Sharfat, K. (2001). Estimation of average milk yield using ranked set sampling. Environmetrics 12
, 395–399.CrossRefGoogle Scholar
Al-Saleh, M. Fraiwan and Zheng, G.
). Estimation of bivariate characteristics using ranked set sampling. The Australian and New Zealand Journal of Statistics 44
, 221–232.CrossRefMathSciNetGoogle Scholar
Al-Saleh, M. Fraiwan and Al-Kadiri, M.
(2000). Double ranked Set Sampling. Statistics and Probability Letters 48
, 205–212.zbMATHCrossRefMathSciNetGoogle Scholar
Barabesi, L. and El-Sharaawi A.
(2001). The efficiency of ranked set sampling for parameter estimation. Statistics and Probability Letters 53
, 189–199.zbMATHCrossRefMathSciNetGoogle Scholar
Bohn, L.L. and Wolfe, D.A.
(1994). The effect of imperfect judgment ranking on properties of procedures based on the ranked set samples analogue of the Mann-Whitey-Wilcoxon statistic. J.Amer.Statist.Assoc. 89
, 168–176.zbMATHCrossRefMathSciNetGoogle Scholar
Dell, T.R. & Clutter, J.L.
(1972). Ranked Set Sampling Theory with Order Statistics Background. Biometrics 28
, 545–555.CrossRefGoogle Scholar
(1988). Group representation in Probability. and Statistics, p. 174.Google Scholar
Fei, H., Sinha, B.K and Wu, Z.
(1994). Estimation of parameters in two-Parameter Weibull and extreme-value distributions using ranked set sampling. Journal of Statistical Research 28
, 149–161.MathSciNetGoogle Scholar
Lam, K., Sinha, B.K. and Wu, Z.
(1994). Estimation of parameters in two-parameter Exponential distribution using ranked set sampling. Annals of the Institute of Statistical Mathematics 46
(4), 723–736.zbMATHCrossRefMathSciNetGoogle Scholar
, E. L. (1983). Theory of point estimation. John Willey and Sons Inc.Google Scholar
Maharota, K.G. and Nanda, P.
(1974) Unbiased estimator of parameter; by order statistics in the case of censored samples, Biometrika 61
, 601–606.CrossRefMathSciNetGoogle Scholar
(1952). A method for unbiased selective sampling using ranked sets. Australian J. Agricul. Research 3
, 385–390.CrossRefGoogle Scholar
Mode, N., Conquest, L. and Marker, D.
(1999). Ranked set sampling for ecological research: Accounting for the total cost of sampling. Environmetrics 10
, 179–194.CrossRefGoogle Scholar
Stokes, S.L. and Sager, T.
(1988). Characterization of ranked set sample with application to estimating distribution functions. Journal of the American Statistical Association 83
, 374–381.zbMATHCrossRefMathSciNetGoogle Scholar
(1980). Estimation of variance using judgment ordered ranked set samples. Bometrics 36
, 35–42.zbMATHCrossRefMathSciNetGoogle Scholar
(1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods A6
, 1207–1211.CrossRefGoogle Scholar
Takahasi, K. and Wakimoto, K.
(1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics 20
, 1–31.zbMATHCrossRefMathSciNetGoogle Scholar
Zheng, G and Al-Saleh
, M. Fraiwan (2000). Modified Maximum Likelihood Estimator based on ranked set sampling. Annals of the Institute of Statistical Mathematics 54
, 641–658CrossRefMathSciNetGoogle Scholar