Weibull-Bayesian analysis based on ranked set sampling

  • Authors

    • Amr Sadek Al-Azhar University
    • Fahad Alharbi Umm Al-Qura University
    2014-10-02
    https://doi.org/10.14419/ijasp.v2i2.3373
  • Abstract

    Most of estimation methods reported in the literature are based on simple random sampling (SRS), which to certain extent is considerably less effective in estimating the parameters as compared to a new sampling technique, ranked set sampling (RSS) and its modifications.

    In this Paper we address the problem of Bayesian estimation of the parameters for Weibull distribution, based on ranked set sampling. Two loss functions have been studied: (i) the squared-error loss function as symmetric loss function, (ii) the linex loss function as asymmetric loss function. Different estimates are compared using simulations for illustrative purposes.

    Keywords: Bayes, Estimation, Loss function, priors, Ranked set sampling.

  • References

    1. G.A. McIntyre, Method of unbiased selective sampling using ranked sets, Australian Journal Agricultural Research, 3(1952) 385–390.
    2. K. Takahasi, K. Wakimoto, On the unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Statist. Math, 20 (1968) 1–31.
    3. T.R. Dell The theory of some applications of ranked set sampling, Ph. D. Thesis, University of Georgia, Athens, GA, USA, 1969.
    4. T.R. Dell, J.L. Clutter, Ranked set sampling theory with order statistics background. Biometrics, 28 (1972) 545–553.
    5. G.P. Patil, A.K. Sinha, C. Taillie, Ranked set sampling: a bibliography, Environ. Ecol. Stat., 6(1) (1999) 91–98.
    6. G.P. Patil, A.K. Sinha, C. Taillie, Ranked set sampling, in: Patil, G.P. and Rao, C.R.(Eds.), Handbook of Statistics. vol. 12, Elsevier, Amsterdam; 1994.
    7. G.D. Johnson , G.P. Patil, A.K. Sinha, Ranked set sampling for vegetation research, Abstarcta Botanica, 17(1-2) (1993) 87–102.
    8. N. Mode, L. Conquest, D. Marker, Ranked set sampling for ecological research: accounting for the total cost of sampling, Environmetrics,10 (1999) 179–194.
    9. L.L. Bohn, D.A. Wolfe, Nonparametric two-sample procedures for ranked set samples data, J. Amer. Statist. Assoc.,87 (1992) 552–561.
    10. L.L. Bohn, D.A. Wolfe, The effect of imperfect judgment rankings on properties of procedures based on the ranked set samples analog of the Mann-Whitney- Wilcoxon statistic, J. Amer. Statist. Assoc., 89 (1994) 168–176.
    11. T.P. Hettmansperger, The ranked set sample sign test. J. Nonparametr. Stat., 4(1995) 263–270.
    12. K.M. Koti, G.J. Babu, Sign test for ranked set sampling. Comm. Statist. Theory Methods, 25(1996) 1617–1630.
    13. L.L. Bohn, A review of nonparametric ranked set sampling methodology, Comm. Statist. Theory Methods,25(1996) 2675–2685.
    14. H.A. Muttlak, M.F. Al-Saleh, Recent developments in ranked set sampling. Pakistan J. Statist., 16(2000) 269–290.
    15. A.A. Jemain, A.I. Al-Omari, K. Ibrahim, Multistage extreme ranked set samples for estimating the population mean. J. Stat. Theory Appl., 6(4) (2007) 456–471.
    16. H. Samawi, M.F. Al-Saleh, O. Al-Saidy, On the matched pairs sign test using bivariate ranked set sampling: an application to environmental issues. Afr. J. Env. Sci. and Tech., 2(1) (2008) 001–009.
    17. N. A. Al-Odat, Modification in Ratio Estimator Using Rank Set Sampling. European J. Sci. Res., 29(2) (2009) 265–268.
    18. S.A. Al-Hadhrami, A.I. Al-Omari, M. F. Al-Saleh, Estimation of standard deviation of normal distribution using moving extreme ranked set sampling. Proc. of academy of science, Eng. and tech., 37(2009) 988–993.
    19. G.E.P Box, G.C. Tiao, Bayesian inference in statistical analysis. Addison Wesley; 1973.
    20. J.O. Berger, Statistical decision theory and bayesian analysis. Springer-Verlag, New York; 1985.
    21. A. Zellner, Bayesian estimation and prediction using asymmetric loss functions. J. Amer. Statist. Assoc., 81(1986) 446–451.
    22. H.R. Varian, A Bayesian Approach to Real Estate Assessment. North Holland, Amsterdam; 1975.
  • Downloads

  • Received date: 2014-08-14

    Accepted date: 2014-09-14

    Published date: 2014-10-02