Z.A. Al-Hemyari∗
[1] A.C. Davison, Statistical models, (UK, Cambridge UniversityPress, 2003). [2] S.K. Sinha, Reliability and life testing (New Delhi, WileyEastern Limited, 1986). [3] D.J. Davis, The analysis of some failure data, Journal of theAmerican Statistical Assosciation, 47, 1952, 113–150. [4] I. Bazovsky, Reliability theory and practice (New Jersey: Pren-tice Hall, 1961). [5] I. Karanta, Expert system in forecast model building, Proc.9th Finish Artificial Intelligence Conf. on AI of tomorrow:Symposium on Theory, Espoo, Finland, 2000, 77–85. [6] N.S. Kambo, B.R. Handa, & Z.A. Al-Hemyari, Double stage403Table 7Eff(˜μ2|μ0) (E1), E(n|˜μ2)(E2), and (100x(n2|n)(pr{X1 ∈ R2}))(E3) α = 0.01, b = 0.001, n1 = 5, 11, and Different Values of nn n1 = 5 n1 = 11E1 E2 E3 E1 E2 E312 83.299 5.010 16.500 110.921 11.010 4.25014 148.058 5.030 37.125 150.972 11.030 12.21416 231.551 5.050 49.500 197.237 11.050 26.93718 334.116 5.070 57.950 249.763 11.070 34.50020 456.225 5.090 63.643 308.603 11.090 40.55022 598.497 5.110 68.063 373.825 11.110 44.50024 761.709 5.130 71.500 445.506 11.130 49.62526 946.813 5.150 74.250 523.737 11.150 53.11528 1155.000 5.170 76.500 608.622 11.170 56.10730 1387.500 5.190 68.375 700.276 11.190 58.70032 1646.000 5.210 79.972 798.827 11.210 60.92934 1932.500 5.230 81.321 905.420 11.230 62.98036 2249.000 5.250 82.500 1017.200 11.250 64.88638 2598.300 5.270 83.531 1137.400 11.270 66.34240 2983.300 5.290 84.441 1565.100 11.290 67.77542 3407.700 5.310 85.250 1400.600 11.310 69.07144 3875.700 5.3300 85.974 1544.100 11.320 70.25056 7859.300 5.450 89.100 2588.600 11.450 74.554shrunken estimator of the mean of a normal distribution, Jour-nal of Information and Optimization Science, 12, 1991, 1–11. [7] C. Stein, A two-sample test for a linear hypothesis whose poweris independent of the variance, The Annals of MathematicalSciences, 16(2), 1945, 45–258. [8] S.K. Katti, Use of some a prior knowledge in the estimationof means from double samples, Biometrics, 18, 1962, 139–147. [9] J.C. Arnold & H.A. Al-Bayyati, On double stage estimation ofthe mean using prior knowledge, Biometrics, 26, 1970, 787–800. [10] V.B. Waiker, F.J. Schuurmann, & T.E. Raghunathan, On atwo stage shrinking testimator of the mean of a normal distri-bution, Communication in Statistics – Theory and Methods,A 13(15), 1984, 1901–1913. [11] V.B. Waiker, M.V. Ratnaparkhi, & F.J. Schuurmann, Im-proving the efficiency of the two stage shrinking estimatorsusing bootstrap methods, Proc. International Conf. on MonteCarlo and Quasi Monte Carlo Methods, Springer, Hong Kong,2001, 1–7 available at: www.galaxy.gmu.edu/interface. [12] N.S. Kambo, B.R. Handa, & Z.A. Al-Hemyari, On Hunts-berger type shrinkage estimator, Communication in Statistics– Theory and Methods, 2(3), 1992, 823–841. [13] H.P. Singh, S. Saxena, & M.R. Espejo, Estimation of standarddeviation in normal parent by shrinkage towards an interval,Journal of Statistical Planning and Inference, 126, 2004,479–493. [14] H.P. Singh & S. Saxena, Estimating fisher information innormal population with prior information, Statistica, LXV,2005, 73–91. [15] S. Saxena & H.P. Singh, From ordinary to shrinkage squareroot estimators, Communication Statistics – Theory andMethods, 35, 2006, 1037–1058. [16] Z.A. Al-Hemyari, A. Khurshid, & A. Al-Joberi, On Thompsontype estimators for the mean of normal distribution, Sent forpublication, Revista Investigacion Operacionl, 30(2), 2009,109–116.
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