346
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

E-Bayesian estimations of the reliability and its E-posterior risk under different loss functions

Pages 1527-1545 | Received 28 Feb 2018, Accepted 03 Jul 2018, Published online: 18 Dec 2018

References

  • Ali, S. 2015. On the Bayesian estimation of the weighted Lindley distribution. Journal of Statistical Computation and Simulation 85 (5):855–80.
  • Ali, S., M. Aslam, and S. M. A. Kazmi. 2013. A study of the effect of the loss function on Bayes estimate, posterior risk and hazard function for Lindley distribution. Applied Mathematical Modelling 37 (8):6068–78.
  • Ando, T., and A. Zellner. 2010. Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct Monte Carlo and importance sampling techniques. Bayesian Analysis 5 (1):65–96.
  • Gholizadeh, R., M. J. P. Barahona, and M. Khalilpour. 2016. Fuzzy E-Bayesian and hierarchical Bayesian estimations on the Kumaraswamy distribution using censoring data. International Journal of Fuzzy System Applications 5 (2):74–95.
  • Gonzalez-Lopez, V. A., R. Gholizadeh, and C. E. Galarza. 2017. E-Bayesian estimation for system reliability and availability analysis based on exponential distribution. Communications in Statistics-Simulation and Computation 46 (8):6221–41.
  • Han, M. 1997. The structure of hierarchical prior distribution and its applications. Chinese Operations Research and Management Science 6 (3):31–40.
  • Han, M. 2007. E-Bayesian estimation of failure probability and its application. Mathematical and Computer Modelling 45 (9–10):1272–9.
  • Han, M. 2009. E-Bayesian estimation and hierarchical Bayesian estimation of failure rate. Applied Mathematical Modelling 33 (4):1915–22.
  • Han, M. 2011. E-Bayesian estimation of the reliability derived from binomial distribution. Applied Mathematical Modelling 35 (5):2419–24.
  • Han, M. 2012. The M-Bayesian credible limits of the reliability and its applications. Communications in Statistics-Theory and Methods 41 :3814–30.
  • Han, M. 2013. Properties of E-Bayesian estimation for the reliability derived from binomial distribution. Acta Mathematica Scientia (Series A) 33(1):62–70.
  • Han, M. 2017. The E-Bayesian and hierarchical Bayesian estimations of Pareto distribution parameter under different loss functions. Journal of Statistical Computation and Simulation 87 (3):577–93.
  • Han, M. 2018. E-Bayesian estimation and its E-MSE under the scaled squared error loss function, for exponential distribution as example. Communications in Statistics-Simulation and Computation. Published online: 25 Feb 2018. doi:10.1080/03610918.2018.1425444.
  • Jaheen, Z. F., and H. M. Okasha. 2011. E-Bayesian estimation for the burr type XII model based on type-2 censoring. Applied Mathematical Modelling 35 (10):4730–7.
  • Karimnezhad, A., and F. Moradi. 2016. Bayes, E-Bayes and robust Bayes prediction of a future observation under precautionary prediction loss functions with applications. Applied Mathematical Modelling 40 (15–16):7051–61.
  • Kazmi, A. M. S., M. Aslam, and S. Ali. 2012. Preference of prior for the class of life-time distribution under different loss functions. Pakistan Journal of Statistics 28 (4):467–84.
  • Kizilaslan, F. 2017. The E-Bayesian and hierarchical Bayesian estimations for the proportional reversed hazard rate model based on record values. Journal of Statistical Computation and Simulation 87:2253–73.
  • Li, G. Y., Q. G. Wu, and Y. H. Zhao. 2002. On Bayesian analysis of binomial reliability growth. Journal of the Japan Statistical Society 32 (1):1–14.
  • Lindley, D. V., and A. F. M. Smith. 1972. Bayes estimates for the linear model. Journal of the Royal Statistical Society (Series B) 34:1–41.
  • Miller, K. W., L. J. Morell, R. E. Noonan, S. K. Park, D. M. Nicol, B. W. Murrill, and M. Voas. 1992. Estimating the probability of failure when testing reveals no failures. IEEE Transactions on Software Engineering 18 (1):33–43.
  • Okasha, H. M. 2014. E-Bayesian estimation for the Lomax distribution based on type-II censored data. Journal of the Egyptian Mathematical Society 22 (3):489–95.
  • Okasha, H. M., and J. Wang. 2016. E-Bayesian estimation for the geometric model based on record statistics. Applied Mathematical Modelling 40 (1):658–70.
  • Osei, F. B., A. A. Duker, and A. Stein. 2011. Hierarchical Bayesian modeling of the space-time diffusion patterns of cholera epidemic in Kumasi, Ghana. Statistica Neerlandica 65 (1):84–100.
  • Parsian, A., and N. Nematollahi. 1996. Estimation of scale parameter under entropy loss function. Journal of Statistical Planning Inference 52 (1):77–91.
  • Reyad, H., A. Younis, and A. Alkhedir. 2016. Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution. International Journal of Advanced Statistics and Probability 4 (1):62–74.
  • Varian, H. R. 1975. A Bayesian approach to real estate assessment. In Studies in Bayesian econometrics and statistics in honor of Leonard J savage, eds. S. E. Feinberge and A. Zellner, 195–208. Amsterdam: North Holland Publishing Co.
  • Yousefzadeh, F. 2017. E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function. Communications in Statistics-Theory and Methods 46 (1):1–8.
  • Zellner, A. 1986. Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association 81 (394):446–51.
  • Zellner, A. 1994. Bayesian and Non-Bayesian estimation using balanced loss functions. In Statistical decision theory and methods V, eds. J. O. Berger and S. S. Gupta, 337–90, New York: Springer-Verlag.
  • Zhang, Y., M. Zhao, S. Zhang, J. Wang, and Y. Zhang. 2017. An integrated approach to estimate storage reliability with initial failures based on E-Bayesian estimates. Reliability Engineering & System Safety 159:24–36.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.