The Moore and Bilikam model and Burr XII sub-model under progressively type-II censoring scheme

Year 2023, Volume: 52 Issue: 3, 768 - 784, 30.05.2023

Mehdi Bazyar Einolah Deiri Ezzatallah Baloui Jamkhaneh

https://doi.org/10.15672/hujms.1082101

Abstract

The Moore and Bilikam family includes lifetime distributions, hence there is a need for a meticulous investigation of the proposed family. We evaluate different estimation procedures for both parameters and reliability function of the Moore and Bilikam family comprehensively, including the maximum likelihood, Bayesian and E-Bayesian estimation methods. The estimation methods of the Moore and Bilikam family are compared via the simulation data, whereas simulation results of the Burr XII sub-model are reported. Based on the simulation approach, we concluded the estimates of the Moore and Bilikam family are convergent to the corresponding parameters, and the root mean square error values derived by the E-Bayesian method are less than other estimators. The analysis of the time between failures of secondary reactor pumps data set has been represented for illustrative purposes, which confirmed simulation results.

Keywords

E-Bayesian estimation, stochastic EM algorithm, Burr XII, Moore and Bilikam family, progressively type-II censoring, failure data

References

• [1] H.H. Ahmad, Best prediction method for progressive type-II censored samples under new Pareto model with applications, J. Math. 2021, Article ID 1355990, 2021.
• [2] A. Algarni, A.M. Almarashi, H. Okasha and H.K.T. Ng, E-Bayesian estimation of Chen distribution based on type-I censoring scheme, Entropy 22, 636, 2020.
• [3] R. Alshenawy, A. Al-Alwan, E.M. Almetwally, A.Z. Afify and H.M. Almongy, Progressive type-II censoring schemes of extended odd Weibull Exponential distribution with applications in medicine and engineering, Mathematics 8 (10), 1–19, 2020.
• [4] M.N. Asl, R.A. Belaghi and H. Bevrani, Classical and Bayesian inferential approaches using Lomax model under progressively type-I hybrid censoring, J. Comput. Appl. Math. 343, 397–412, 2018.
• [5] M. Aslam, F. Noor and S. Ali, Shifted exponential distribution: Bayesian estimation, prediction and expected test time under progressive censoring, J. Test. Eval. 48 (2), 1576–1593, 2020.
• [6] N. Balakrishnan and A. Sandhu, A simple simulation algorithm for generating progressive type-II censored sample, Am. Stat. 49 (2), 229–230, 1995.
• [7] V.G. Cancho, F. Louzada-Neto and G.D. Barriga, The poisson-exponential lifetime distribution, Comput. Stat. Data. Anal. 55 (1), 677–686, 2011.
• [8] A. Chaturvedi, B. Devi and and R. Gupta, Robust Bayesian analysis of Moore and Bilikam family of lifetime distributions, Int. J. Agric. Stat. Sci. 15 (2), 497–522, 2019a.
• [9] A. Chaturvedi, S.-B. Kang and A. Malhotra, Preliminary test estimators and confidence intervals for the parametric functions of the Moore and Bilikam family of lifetime distributions based on records, Austrian J. Stat. 48 (4), 58–89, 2019b.
• [10] A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Series B. 39 (1), 1–38, 1977.
• [11] S. Dey, S. Singh, Y.M. Tripathi and A. Asgharzadeh, Estimation and prediction for a progressively censored generalized inverted exponential distribution, Stat. Methodol. 32, 185–202, 2016.
• [12] E.S.A. El-Sherpieny, E.M. Almetwally and H.Z. Muhammed Bayesian and non- Bayesian estimation for the parameter of bivariate generalized Rayleigh distribution based on clayton copula under progressive type-II censoring with random removal, Sankhya A. 10.1007/s13171-021-00254-3, 2021.
• [13] M. Han, The structure of hierarchical prior distribution and its applications, Chin. Operat. Res. Manage. Sci. 6 (3), 31–40, 1997.
• [14] P.W. Jones and S.K. Ashour, Bayesian estimation of the parameters of the mixed exponential distribution from censored samples, Biom. J. 18 (8), 633–637, 2007.
• [15] A.H. Moore and J.E. Bilikam, Bayesian estimation of parameters of life distributions and reliability from type II censored samples, IEEE Trans. Reliab. 27, 64–67, 1978.
• [16] N. Mukhopadhyay, A. Chaturvedi and A. Malhotra, Two-stage procedures for the bounded risk point estimation of the parameter and hazard rate in two families of distributions, Seq. Anal. 37 (1), 69–89, 2018.
• [17] A. Mustafa, B.S. Desouky and S. AL-Garash, The Weibull Generalized flexible Weibull extension distribution, Data Sci. J. 14 (3), 453–478, 2017.
• [18] F.S. Nielsen, The stochastic EM algorithm: estimation and asymptotic results, Bernoulli 6, 457–489, 2000.
• [19] A. Rabie and J. Li, E-Bayesian estimation based on Burr-X generalized type-II hybrid censored data, Symmetry 11 (5), 626, 2019.
• [20] H.M. Reyad and A. So, Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-II censoring, Int. j. adv. math. sci. 4 (1), 10–17, 2016.
• [21] S. Singh and Y.M. Tripathi, Estimating the parameters of an inverse Weibull distribution under progressive type-I interval censoring, Stat. Pap. 59 (1), 21–56, 2018.
• [22] A.A. Soliman, Estimators for the finite mixture of Rayleigh model based on progressively censored data, Commun. Stat.-Theory Methods. 35 (5), 803–820, 2006.
• [23] Q. Yin and H. Liu, Bayesian estimation of geometric distribution parameter under the scaled squared error loss function, IEEE Int. Environ. Sci. and Inf. Appl. Technol. 2010, 650–653, 2010.