Bayesian Estimation of Parameter For Different Loss Functions Using Progressive Type-II Censored Data


Abstract


In this present work, we are going to show the various useful propertiesof the existing distribution known as MG_Exp(ε)-distribution which have notquoted by the host authors like moments, mean deviation about mean, meandeviation about median, order statistics, count of uncertainty. Estimation procedures have been adopted under Bayesian estimation for progressive Type-II censored case. Simulation study has also been carried out to judge the behaviour of the Bayes estimator at the long-run. Performance of the Bayes estimators and their posterior risks of the considered loss functions have been obtained, reported and compared for the considered values of sample size, effective sample size, parameter and removals. The comparison of Bayes estimators of all 6 chosen loss functions have been done on the groundof lowest posterior risks.

DOI Code: 10.1285/i20705948v16n3p519

Keywords: Bayesian estimation, MG_Exp(ε)-distribution, loss function, posterior risk, censoring scheme.

References


Ali, S., Aslam, M., and Kazmi, S. M. A. (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{6078.

Ali Kazmi, S. M., Aslam, M., and Ali, S. (2012). Preference of prior for the class of life-time distributions under different loss functions. Pakistan Journal of Statistics, 28(4).

Balakrishnan, N. (2007). Progressive censoring methodology: an appraisal. Test, 16(2):211{259.

Balakrishnan, N. and Aggarwala, R. (2000). Progressive censoring: theory, methods, and applications. Springer Science & Business Media.

Balakrishnan, N. and Hossain, A. (2007). Inference for the type ii generalized logistic distribution under progressive type ii censoring. Journal of Statistical Computation and Simulation, 77(12):1013{1031.

Feroze, N., Aslam, M., Khan, I. H., and Khan, M. H. (2021). Bayesian reliability estimation for the topp{leone distribution under progressively type-ii censored samples. soft Computing, 25(3):2131{2152.

Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modeling failure time data by lehman alternatives. Communications in Statistics-Theory and methods, 27(4):887{904.

Krishna, H. and Kumar, K. (2013). Reliability estimation in generalized inverted exponential distribution with progressively type ii censored sample. Journal of Statistical Computation and Simulation, 83(6):1007{1019.

Krishna, H. and Malik, M. (2012). Reliability estimation in maxwell distribution with progressively type-ii censored data. Journal of Statistical Computation and Simulation, 82(4):623{641.

Kumar, D., Kumar, P., Kumar, P., Singh, S. K., and Singh, U. (2021). Pcm transformation: Properties and their estimation. Journal of Reliability and Statistical Studies, pages 373{392.

Kumar, D., Kumar, P., Kumar, P., Singh, U., and Chaurasia, P. K. (2020). A new asymmetric loss function for estimation of any parameter. International Journal of Agricultural and Statistical Sciences, 16(2):489{501.

Kumar, D., Kumar, P., Singh, S. K., and Singh, U. (2019). A new asymmetric loss function: estimation of parameter of exponential distribution. J Stat Appl Probab Lett, 6(1):37{50.

Kumar, D., Singh, U., and Singh, S. (2017). Life time distribution: derived from some minimum guarantee distribution, sohag j. Math, 4(1):7{11.

Kumar, D., Singh, U., and Singh, S. K. (2015, a). A method of proposing new distribution and its application to bladder cancer patients data. J. Stat. Appl. Pro. Lett,2(3):235{245.

Kumar, D., Singh, U., and Singh, S. K. (2015, b). A new distribution using sine function its application to bladder cancer patients data. Journal of Statistics Applications & Probability, 4(3):417.

Kundu, D. and Pradhan, B. (2009). Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring. Communications in Statistics-Theory and Methods, 8(12):2030{2041.

Legendre, A. (1805). New methods for the determination of orbits of comets. Courcier, Paris.

Lin, C.-T., Wu, S. J., and Balakrishnan, N. (2006). Inference for log-gamma distribution based on progressively type-ii censored data. Communications in Statistics-Theory and Methods, 35(7):1271{1292.

Norstrom, J. G. (1996). The use of precautionary loss functions in risk analysis. IEEE Transactions on reliability, 45(3):400{403.

Rahman, J., Aslam, M., and Ali, S. (2013). Estimation and prediction of inverse lomax model via bayesian approach. Caspian Journal of Applied Sciences Research, 2(3):43{56.

Rastogi, M. K., Tripathi, Y. M., and Wu, S.-J. (2012). Estimating the parameters of a bathtub-shaped distribution under progressive type-ii censoring. Journal of Applied Statistics, 39(11):2389{2411.

Renyi, A. (1961). On measures of entropy and information. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, pages 547{561. University of California Press.

Sen, S., Chandra, N., and Maiti, S. S. (2018). Survival estimation in xgamma distribution under progressively type-ii right censored scheme. Model Assisted Statistics and Applications, 13(2):107{121.

Singh, S. K., Singh, U., and Kumar, D. (2013). Bayesian estimation of parameters of inverse weibull distribution. Journal of Applied statistics, 40(7):1597{1607.

Wu, S.-J. (2008). Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring. Journal of Applied Statistics, 35(10):1139{1150.


Full Text: pdf
کاغذ a4
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.