E-Bayesian estimation and the corresponding E-MSE under progressive type-II censored data for some characteristics of Weibull distribution
Abstract
Estimating the parameters (or characteristics) of a distribution, from the availability of censored samples, is one of the most important topics in statistical inference over the past decades. This study is concerned about the E-Bayesian estimation method to compute the estimates of the parameter, the hazard rate function and the reliability function of the Weibull distribution when the progressive type-2 censored samples are available. The estimations are obtained based on the Squared error loss function (as a symmetric loss) and General Entropy and LINEX loss functions (as asymmetric losses). In addition, the asymptotic behaviour of the derived E-Bayesian estimators is discussed. Moreover, the E-Bayesian estimators under the different loss functions have been compared through Monte Carlo simulation studies by calculating the E-MSE of the resulting estimators, which is a new measure to compare the E-Bayesian estimators. As an application, we analyzed two real data sets that follow from the Weibull distribution.References
A.A. Abdel-Ghaly, and A.F. Attia, On a new density function, Microelectronics and Reliability, vol. 33, no. 5, pp. 671–679, 1993.
B. Al-Zahrani, and M. Ali, Recurrence relations for moments of multiply type-II censored order statistics from Lindley distribution with applications to inference, Statistics, Optimization and Information Computing, vol. 2, pp. 147–160, 2014.
E. M. Almetwally, M. A. Sabry, R. Alharbi, D. Alnagar, S. A. Mubarak and E. H. Hafez, Marshall–olkin alpha power Weibull
distribution: different methods of estimation based on type-I and type-II censoring, Complexity, 2021.
A. Asgharzadeh, R. Valiollahi, and M. Z. Raqab, Estimation of P r(Y < X) for the two-parameter generalized exponential records, Communications in Statistics-Simulation and Computation, vol. 46, no. 1, pp. 379–394, 2020.
R. Athirakrishnan, and E. Abdul-Sathar, E-Bayesian and hierarchical Bayesian estimation of inverse Rayleigh distribution, American Journal of Mathematical and Management Sciences, pp. 1–22, 2021.
N. Balakrishnan, Progressive censoring methodology:an appraisal (with discussions), Test, vol. 16, no. 2, pp. 211–259, 2007. .
N. Balakrishnan, N. Balakrishnan, and R. Aggarwala, Progressive censoring: theory, methods, and applications, Springer Science & Business Media, 2000.
N. Balakrishnan, and E. Cramer, The art of progressive censoring, Statistics for industry and technology, 2014.
S.K. Bhattacharya, and R.K. Tyagi, Bayesian survival analysis based on the Rayleigh model, Trabajos de Estadistica, vol. 5, no. 1, pp. 81–92, 1990.
D. Demiray, and F. Kızılaslan, Stress–strength reliability estimation of a consecutive k-out-of-n system based on proportional hazard rate family, Journal of Statistical Computation and Simulation, pp. 1–32, 2021.
A. Diamoutene, F. Noureddine, B. Kamsu-Foguem, and D. Barro, Reliability Analysis with Proportional Hazard Model in Aeronautics, International Journal of Aeronautical and Space Sciences, pp. 1–13, 2021.
F.J., Zeinhum and M.O., Hassan E-Bayesian estimation for the Burr type XII model based on type-2 censoring, Applied
Mathematical Modelling, vol. 35, no. 10, pp. 4730–4737, 2011.
N. Feroze, M. Aslam, I. H. Khan, and M.H. Khan, Bayesian reliability estimation for the Topp-Leone distribution under progressively type-II censored samples, Soft Computing, vol. 25, no. 3, pp. 2131–2152, 2021.
D., Kundu and R. D. Gupta, Estimation of P[Y < X] for Weibull distributions, IEEE Trans. Reliab., vol. 55, no. 2, pp. 270–280, 2006.
M. Han, 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, vol. 48, no. 6, pp. 1880–1890, 2019.
M. Han, The structure of hierarchical prior distribution and its applications, Chinese Operations Research and Management Science, vol. 6, no. 3, pp. 31–40, 1997.
M. Han, E-Bayesian estimation of failure probability and its application, Mathematical and Computer Modelling, vol. 45, no. 9-10, pp. 1272–1279, 2007.
N. Jana and S. Bera, Interval estimation of multicomponent stress-strength reliability based on inverse Weibull distribution, Mathematics and Computers in Simulation, vol. 191, pp. 95–119, 2022.
R. Jiang, A novel parameter estimation method for the Weibull distribution on heavily censored data, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol. 236, no. 2, pp. 307–316, 2022.
W. Jianhua, L. Dan and C. Difang, E-Bayesian Estimation and Hierarchical Bayesian Estimation of the System Reliability Parameter, Systems Engineering Procedia, vol. 3, pp. 282–289, 2012.
T. Kayal, Y.M. Tripathi, D. Kundu, and M. Rastogi, Statistical inference of Chen distribution based on type I progressive hybrid censored Samples, Statistics, Optimization and Information Computing, 2019.
J. g. Ma, L. Wang, Y.M. Tripathi, and M.K. Rastogi, Reliability inference for stress-strength model based on inverted exponential Rayleigh distribution under progressive Type-II censored data, Communications in Statistics-Simulation and Computation, pp. 1–25, 2021.
A. B. Mastor, O. Ngesa, J. Mung’atu, N. M. Alfaer and A. Z. Afify, The Extended Exponential Weibull Distribution: Properties, Inference, and Applications to Real-Life Data, Complexity, 2022.
H. Z. Muhammed and E. M. Almetwally, Bayesian and non-Bayesian estimation for the bivariate inverse weibull distribution under progressive type-II censoring, Annals of Data Science, pp. 1–32, 2020.
H. Okasha, Y. Lio, and M. Al-bassam, On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme, Journal of Mathematics, vol. 9, no. 22, pp. 2903, 2021.
J. Ren, and W. Gui, Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution, Computational Statistics, vol. 36, no. 1, pp. 479–513, 2021.
R. Valiollahi, A. Asgharzadeh, and M.Z. Raqab, Estimation of P(Y < X) for Weibull distribution under progressive Type-II censoring, Communications in Statistics-Theory and Methods, vol. 42, no. 24, pp. 4476–4498, 2013.
H.R. Varian, A Bayesian approach to real estate assessment, Studies in Bayesian econometric and statistics in Honor of Leonard J. Savage, pp. 195–208, 1975.
H. Panahi, Reliability analysis for stress-strength model from inverted exponentiated Rayleigh based on the hybrid censored sample, International Journal of Quality & Reliability Management, 2022.
A. Pak, G.A. Parham and M. Saraj, Inference for the Weibull distribution based on fuzzy data, Revista Colombiana de Estadistica, vol. 36, no. 2, pp. 337–356, 2013.
O. Shojaee, H. Piriaei and M.Babanezhad, E-Bayesian Estimations and Its E-MSE For Compound Rayleigh Progressive Type-II Censored Data, Statistics, Optimization & Information Computing, vol. 10, no. 4, pp. 1056–1071, 2022.
O. Shojaee, R. Azimi and M.Babanezhad, Empirical Bayes estimators of parameter and reliability function for compound Rayleigh distribution under record data, American Journal of Theoretical and Applied Statistics, vol. 1, no. 1, pp. 12–15, 2012.
R. Vila and M. Niyazi C¸ ankaya, A bimodal Weibull distribution: properties and inference, Journal of Applied Statistics, vol. 49, no.12, pp. 3044–3062, 2022.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
