E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

  • Authors

    • Hesham Reyad Lecture in EL Qassim University
    • Soha Othman Ahmed
    2015-09-05
    https://doi.org/10.14419/ijams.v3i2.5093
  • E-Bayesian Estimates, Gumbel Type-II Distribution, Loss Functions, Monte Carlo Simulation, Type-II Censoring.

  • Abstract

    This paper seeks to focus on Bayesian and E-Bayesian estimation for the unknown shape parameter of the Gumbel type-II distribution based on type-II censored samples. These estimators are obtained under symmetric loss function [squared error loss (SELF))] and various asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF), Quadratic loss function (QLF) and minimum expected loss function (MELF)]. Comparisons between the E-Bayesian estimators with the associated Bayesian estimators are investigated through a simulation study.

  • References

    1. [1] E. J. Gumbel, Statistics of Extremes, published Colombia University Press, New York, 1973.

      [2] S. Kotz, S. Nadarajah, Extreme value distributions, Theory and Applications. Empirical Col Press, 2000.

      [3] G. Corsini, F. Gini, M. V. Gerco, Cramer-Rao bounds and estimation of the parameters of the Gumbel distribution, IEEE 31 (2002) 1202-1204.

      [4] I. Malinowska, D. Szynal, on characterizations of certain distributions of kth lower (upper) record values. Applied Mathematics and Computation 202, 1 (2008) 338-347. http://dx.doi.org/10.1016/j.amc.2008.02.022.

      [5] N. Feroze, M. Aslam, Bayesian analysis of Gumbel type II distribution under doubly censored samples using different loss functions, Caspian Journal of Applied Sciences Research 1, 10 (2012) 1-10.

      [6] V. Salinas, P. Perez, E. Gonzaled, H. Vaquera, Goodness of Fit Tests for the Gumbel Distribution with Type II right Censored data, Revista Colobiana de Estadistica 35, 3 (2012) 409-424.

      [7] K. Abbas, J. Fu, Y. Tang, (2013). Bayesian Estimation of Gumbel Type-II Distribution, Data Science Journal 12 (2013) 33-46. http://dx.doi.org/10.2481/dsj.13-022.

      [8] N. Feroze, M. Aslam, Bayesian estimation of Two-Component Mixture of Gumbel Type II distribution under Informative Priors, International Journal of Advanced Science and Technology 53 (2013) 11-30.

      [9] M. Han, Expected Bayesian Method for Forecast of Security Investment, Journal of Operations Research and Management Science 14, 5 (2005) 89-102.

      [10] Z. F. Jaheen, H. M. and Okasha, E-Bayesian Estimation for the Burr type XII model based on type-2 censoring. Applied Mathematical Modelling 35 (2011) 4730 - 4737. http://dx.doi.org/10.1016/j.apm.2011.03.055.

      [11] J. Wang, D. li, D. Chen, E-Bayesian Estimation and Hierarchical Bayesian Estimation for Estate Probability in Engineering, Journal of System Engineering procedia 5 (2012) 349-354.

      [12] R. Azimi, F. Yaghmael, B. Fasihi, E-Bayesian Estimation based on generalized half Logestic progressive type-II censored data, International Journal of Advanced Mathematical Science 1, 2 (2013) 56-63.

      [13] H. M. Okasha, E-Bayesian Estimation for the Lomax distribution based on type-II censored data, Journal of the Egyptian Mathematical Society 22, 3 (2014) 489-495. http://dx.doi.org/10.1016/j.joems.2013.12.009.

      [14] A. Mood, F. A. Graybill, D. Boes, Introduction to the Theory of Statistics. McGraw-Hill Series in Probability and Statistics, 1974.

      [15] A. Zellner, Bayesian estimation and Prediction using Asymmetric loss Function. Journal of American Statistical Association 81 (1986) 446-451. http://dx.doi.org/10.1080/01621459.1986.10478289.

      [16] M. H. Degroot, Optimal Statistical Decision. McGraw-Hill Inc, (1970).

      [17] V. M. Tummala, P. T. Sathe, Minimum expected loss estimators of reliability and parameters of certain lifetime distributions. IEEE Tran-sactions on Reliability 27, 4 (1978) 283285.

      [18] M. Han, The structure of hierarchical prior distribution and its applications, Chinese Operations Research and Management Science 6, 3 (1997) 31-40.

      [19] M. Han, E- Bayesian estimation and hierarchical Bayesian estimation of failure rate. Applied Mathematical Modelling 33 (2009) 1915-1922. http://dx.doi.org/10.1016/j.apm.2008.03.019.

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  • How to Cite

    Reyad, H., & Ahmed, S. O. (2015). E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme. International Journal of Advanced Mathematical Sciences, 3(2), 108-120. https://doi.org/10.14419/ijams.v3i2.5093