On double stage minimax-shrinkage estimator for generalized Rayleigh model

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a0) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .

    In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.

    The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(×) and suitable region R.

    Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.

    Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.

    Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.

  • Keywords

    Generalized Rayleigh Distribution, Maximum Likelihood Estimator, Minimax Estimator, Double Stage Shrinkage Estimator, Mean Squared Error and Relative Efficiency.

  • References

      [1] Al-Joboori, A.N., (2010), Pre-Test Single and Double Stage Shrunken Estimators for the Mean of Normal Distribution with Known Variance, Baghdad Journal for Science, Vol.7(4), pp.1432-1442.

      [2] Al-Joboori, A.N., et al (2014), Single and Double Stage Shrinkage Estimators for the Normal Mean with the Variance Cases , International Journal of Statistics , Vol.(38),2,PP,1127 -1134.

      [3] Aludaat 1, K.M., Alodat, M.T. and Alodat, T.T., (2008), Parameter Estimation of Burr Type X Distribution for Grouped Data, Applied Math. Sci., Vol. 2 (9), pp.415-423.

      [4] Burr, I.W., (1942), Cumulative Frequency Distribution, Annals of Mathematical Statistics, Vol. (13), pp.215-232.

      [5] Iman Makhdoom, (2011), Minimax Estimation of the Parameter of the Generalized Exponential Distribution, International Journal of Academic Research, Vol.3 (2), pp.515-527.

      [6] Katti, S.K., (1962), Use of Some a Prior Knowledge in the Estimation of Means from Double Samples, Biometrics, Vol.18, pp.139-147. http://dx.doi.org/10.2307/2527452.

      [7] Kundu, D. and Raqab, M.Z., (2005), Generalized Rayleigh Distribution: Deferent Methods of Estimation, Computational Statistics and Data Analysis, Vol.49, pp.187-200. http://dx.doi.org/10.1016/j.csda.2004.05.008.

      [8] Lanpong Li ,(2013), Minimax Estimation of Generalized Exponential Distribution under Square Log Error Loss and MLINEX Loss Function , Research Journal of Mathematics and Statistics, Vol.5(3),pp.24-27.

      [9] Maha.A.Mohammed, (2011), Double Stage Shrinkage Estimator of Two Parameters Generalized Rayleigh Distribution, Education college journal AL-Mustansiriya University, Vol. (2), pp.566-573.

      [10] Masoud Yarmohammadi and Hassan Pazira ,(2010),Minimax Estimation of the Parameter of the Burr Type Xii Distribution, Australian Journal of Basic and Applied Sciences, Vol.4(12), pp.6611-6622.

      [11] M.Kamruj Jaman Bhuiyan ,et al,(2007) ,Minimax Estimation of the Parameter of the Rayleigh Distribution , Festschrift in honor Distinguished Professor Mir Masson Ali on the occasion of his retirement,pp.207-212.

      [12] Raqab, M.Z., (1998), Order Statistics from the Burr Type X Model, Computers Mathematics and Applications, Vol.36, pp.111-120. http://dx.doi.org/10.1016/S0898-1221(98)00143-6.

      [13] Raqab, M.Z. and Kundu, D., (2006), Burr Type X Distribution, Revisited, Journal of Probability and Statistical Sciences, Vol.4 (2), pp.179-193.

      [14] Rodriguez, R.N., (1977), A Guide to Burr Type XII Distributions, Biometrika, Vol.64, pp.129-134. http://dx.doi.org/10.1093/biomet/64.1.129.

      [15] Surles, J.G. and Padgett, W.J., (2001), Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution, Lifetime Data Analysis, Vol.7, pp.187-200. http://dx.doi.org/10.1023/A:1011352923990.

      [16] Surles, J.G. and Padgett, W.J., (2005), Some Properties of a Scaled Burr Type X Distribution, Journal of Statistical Planning and Inference, Vol.72, pp.271-280. http://dx.doi.org/10.1016/j.jspi.2003.10.003.

      [17] Thompson, J.R., (1968), Some Shrinkage Techniques for Estimating the Mean, J. Amer. Statist. Assoc, Vol.63, pp.113-122.

      [18] Waikar, V.B., Schuurmann, F.J. and Raghunathar, T.E., (1984), On a Two-Stage Shrinkage Testimator of the Mean of a Normal Distribution, Commum. Statist-Theory. Meth. A, Vol.13 (15), pp.1901-1913. http://dx.doi.org/10.1080/03610928408828802.

      [19] Wingo, D.R., (1993), Maximum Likelihood Methods for fitting the Burr Type XII Distribution to Multiply (Progressively) Censored Life Test Data, Metrika, Vol. 40, pp.203-210. http://dx.doi.org/10.1007/BF02613681.




Article ID: 5553
DOI: 10.14419/ijamr.v5i1.5553

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.