255
Views
5
CrossRef citations to date
0
Altmetric
Article

Assessing the effect of E-Bayesian inference for Poisson inverse exponential distribution parameters under different loss functions and its application

, , &
Pages 5763-5805 | Received 27 Jan 2020, Accepted 31 Oct 2020, Published online: 25 Nov 2020

References

  • Aarset, M. V. 1987. How to identify a bathtub hazard rate. IEEE Transactions on Reliability R-36 (1):106–108.
  • Aggarwala, R., and N. Balakrishnan. 1998. Some properties of progressive censored order Statistics from arbitrary and uniform distributions with applications. Journal of Statistical Planning and Inference 70 (1):35–49.
  • Balakrishnan, N. 2007. Progressive censoring methodology: An appraisal. TEST 16 (2):211–59.
  • Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring: Theory, methods, and applications. New York: Springer Science & Business Media.
  • Balakrishnan, N., and E. Cramer. 2014. The art of progressive censoring: Applications to reliability and quality. New York: Springer.
  • Balakrishnan, N., and N. Kannan. 2001. Ch. 14. Point and Interval estimation for parameters of the Logistic distribution based on progressively type-II censored samples. Handbook of Statistics 20:431–56.
  • Balakrishnan, N., and R. A. Sandhu. 1995. A simple simulational algorithm for generating progressive type-II censored samples. The American Statistician 49 (2):229–30.
  • Barreto-Souza, W., and F. Cribari-Neto. 2009. A generalization of the Exponential-Poisson distribution. Statistics and Probability Letters 79 (24):2493–500.
  • Berger, J. O. 2013. Statistical decision theory and Bayesian analysis. New York: Springer Science & Business Media.
  • Calabria, R., and G. Pulcini. 1990. On the maximum likelihood and least-squares estimation in the inverse Weibull distributions. Statistica Application 2 (1):53–66.
  • Childs, A., and N. Balakrishnan. 2000. Conditional inference procedures for the Laplace distribution when the observed samples are progressively censored. Metrika 52 (3):253–65.
  • Cohen, A. C. 1963. Progressively censored samples in life testing. Technometrics 5 (3):327–39.
  • Collett, D. 2015. Modelling survival data in medical research, volume 3. New York: Chapman and Hall/CRC.
  • El-Sagheer, R. M. 2017. E-Bayesian estimation for Rayleigh model using progressive type-II censoring data. Journal of Statistical Theory and Applications 16 (2):239–47.
  • Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. New York: Chapman and Hall/CRC.
  • Gholizadeh, R., M. Khalilpor, and M. Hadian. 2011. Bayesian estimations in the Kumaraswamy distribution under progressively type-II censoring data. International Journal of Engineering, Science and Technology 3 (9):47–65.
  • Gupta, I. 2017. Bayesian and E-Bayesian method of estimation of parameter of Rayleigh distribution-A Bayesian approach under linex loss function. International Journal of Statistics and Systems 12 (4):791–96.
  • 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):1272–79.
  • Han, M. 2011a. E-Bayesian estimation and hierarchical Bayesian estimation of failure probability. Communications in Statistics-Theory and Methods 40 (18):3303–14.
  • Han, M. 2011b. Estimation of failure probability and its applications in lifetime data analysis. International Journal of Quality, Statistics, and Reliability 2011:1–6.
  • Han, M. 2017a. The E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter. Communications in Statistics-Theory and Methods 46 (4):1606–20.
  • Han, M. 2017b. 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. 2019a. 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 48 (6):1880–90.
  • Han, M. 2019b. E-Bayesian estimation of the exponentiated distribution family parameter under linex loss function. Communications in Statistics-Theory and Methods 48 (3):648–59.
  • Han, M. 2019c. E-Bayesian estimations of parameter and its evaluation standard: E-MSE (expected mean square error) under different loss functions. Communications in Statistics-Simulation and Computation. Advance online publication. doi:10.1080/03610918.2019.1589510.
  • Han, M. 2020a. E-Bayesian estimations of the reliability and its E-posterior risk under different loss functions. Communications in Statistics-Simulation and Computation 49 (6):1527–45.
  • Han, M. 2020b. E-Bayesian estimation and its E-posterior risk of the exponential distribution parameter based on complete and type I censored samples. Communications in Statistics - Theory and Methods 49 (8):1858–72. doi:10.1080/03610926.2019.1565837.
  • Huang, S. R., and S. J. Wu. 2012. Bayesian estimation and prediction for Weibull model with progressive censoring. Journal of Statistical Computation and Simulation 82 (11):1607–20.
  • Ihaka, R., and R. Gentleman. 1996. R A language for data analysis and graphics. Journal of Computational and Graphical Statistics 5:299–314.
  • Jaheen, Z. F., and H. M. Okasha. 2011. E-Bayesian estimation for the Burr type-XII model based on type-II censoring. Applied Mathematical Modelling 35 (10):4730–37.
  • Kamps, U., and E. Cramer. 2001. On distributions of generalized order statistics. Statistics 35 (3):269–80.
  • Kim, C., and K. Han. 2009. Estimation of the scale parameter of the Rayleigh distribution under general progressive censoring. Journal of the Korean Statistical Society 38 (3):239–46.
  • Kim, C., J. Jung, and Y. Chung. 2011. Bayesian estimation for the exponentiated Weibull model under type-II progressive censoring. Statistical Papers 52 (1):53–70.
  • Kızılaslan, 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 (11):2253–73.
  • Kumar, D., U. Singh, S. K. Singh, and G. Bhattacharyya. 2015. Bayesian estimation of exponentiated Gamma parameter for progressive type-II censored data with Binomial removals. Journal of Statistics Applications and Probability 4 (2):265.
  • Kumar, M., A. Pathak, and S. Soni. 2019. Bayesian inference for Rayleigh distribution under step-stress partially accelerated test with progressive type-II censoring with Binomial removal. Annals of Data Science 6 (1):117–52.
  • Kumar, M., S. K. Singh, and U. Singh. 2018. Bayesian inference for Poisson-inverse exponential distribution under progressive type-II censoring with Binomial removal. International Journal of System Assurance Engineering and Management 9 (6):1235–49.
  • Kundu, D. 2008. Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring. Technometrics 50 (2):144–54.
  • Lindley, D. V., and A. F. Smith. 1972. Bayes estimates for the linear model. Journal of the Royal Statistical Society: Series B (Methodological) 34 (1):1–18.
  • Louzada-Neto, F., V. G. Cancho, and G. D. C. Barriga. 2011. The Poisson-exponential distribution: A Bayesian approach. Journal of Applied Statistics 38 (6):1239–48.
  • Lu, W., and D. Shi. 2012. A new compounding life distribution: The Weibull-Poisson distribution. Journal of Applied Statistics 39 (1):21–38.
  • Metropolis, N., and S. Ulam. 1949. The Monte Carlo method. Journal of the American Statistical Association 44 (247):335–41. doi:10.1080/01621459.1949.10483310.
  • 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.
  • Reyad, H. M., and S. O. Ahmed. 2016. Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-II censoring. International Journal of Advanced Mathematical Sciences 4 (1):10–17.
  • Singh, S.,. U. Singh, M. Kumar, and P. Vishwakarma. 2014. Classical and Bayesian inference for an extension of the Exponential distribution under progressive type-II censored data with Binomial removals. Journal of Statistics Applications & Probability Letters 1 (3):75–86.
  • Singh, S. K., U. Singh, and V. K. Sharma. 2013. Expected total test time and Bayesian estimation for generalized Lindley distribution under progressively type-II censored sample where removals follow the Beta-Binomial probability law. Applied Mathematics and Computation 222:402–19.
  • Tse, S. K., C. Y, and H. K. Yuen. 2000. Statistical analysis of Weibull distributed lifetime data under type II progressive censoring with Binomial removals. Journal of Applied Statistics 27 (8):1033–43.
  • Varian, H. R. 1975. A Bayesian approach to real estate assessment. Amsterdam: North Holland Publishing Co, 36(1):195–208.
  • Wu, S. J., and C. T. Chang. 2002. Parameter estimations based on Exponential progressive type II censored data with Binomial removals. International Journal of Information and Management Sciences 13 (3):37–46.
  • 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 related topics V, 377–90. New York: Springer.

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.