E-Bayesian estimation of parameters of inverse Weibull distribution based on a unified hybrid censoring scheme

Document Type : Review articles

Authors

1 Department of Statistics‎, ‎Payame Noor University‎, ‎P‎. ‎O‎. ‎Box 19395-4697‎, ‎Tehran‎, ‎Iran

2 Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Guilan‎, ‎Rasht‎, ‎Iran

3 Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

Abstract

‎The combination of generalization Type-I hybrid censoring and generalization Type-II hybrid censoring schemes create a new censoring called a unified hybrid censoring scheme‎. ‎Therefore‎, ‎in this study‎, ‎the E-Bayesian estimation of parameters of the inverse Weibull distribution is obtained under the unified hybrid censoring scheme‎, ‎and the efficiency of the proposed method was compared with the Bayesian estimator using Monte Carlo simulation and a real data set‎.

Keywords

[1] N. Balakrishnan, A. Rasouli and N.S. Farsipour, Exact likelihood inference based on a unified hybrid censored sample from the exponential distribution, J. Stat. Comput. Simul. 78 (2008) 475–488.
[2] R. Calabria and G. Pulcini, Bayes 2-sample prediction for the inverse Weibull distribution, Commun. Stat. Theory Methods. 23 (1994) 1811–1824.
[3] B. Chandrasekhar, A. Childs and N. Balakrishnan, Exact Likelihood Inference for the Exponential distribution under Generalized Type-I and Type-II Hybrid Censoring, Nav. Res. Logist. 51 (2004) 994–1004.
[4] A. Childs, B. Chandrasekhar, N. Balakrishnan and D. Kundu, Exact Likelihood Inference Based on Type-I and Type-II Hybrid Censored Samples from the Exponential distribution, Ann. Inst. Stat. Math. 55 (2003) 319–330.
[5] P. Congdon, Bayesian Statistical Modeling, Wiley, NewYork, 2001.
[6] B. Epstein, Truncated life tests in the exponential case, Ann. Math. Stat. 25 (1954) 555–564.
[7] P. Erto and M. Rapone, Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model, Reliab. Eng. 7 (1984) 181–191.
[8] M.E. Flygare and J.A. Buckwalter, Maximum likelihood estimation for the two-parameter Weibull distribution based on interval data, IEEE Trans. Reliab. 34 (2008) 57-60.
[9] C.B. Guure, N.A. Ibrahim, and A.M. Al-Omari, Bayesian estimation of two-parameter Weibull distribution using extension of Jeffreys’ prior information with three loss functions, Math. Probl. Eng. 2012 (2012) Article ID 589640,1-13.
[10] M. Han, The structure of hierarchical prior distribution and its applications, Chinese. Oper. Res. Manage. Sci. 63 (1997) 31–40.
[11] M. Han, E-Bayesian estimation and hierarchical Bayesian estimation of failure rate, Appl. Math. Model. 33 (2009) 1915–1922.
[12] M. Han, E-Bayesian estimation of the reliability derived from Binomial distribution, Appl. Math. Model. 35 (2011) 2419–2424.
[13] M. Han, The E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter, Commun. Stat. Theory Methods. 46 (2017) 1606–1620.
[14] Z.F. Jaheen and H.M. Okasha, E-Bayesian estimation for the Burr type XII model based on type-II censoring, Appl. Math. Model. 35 (2011) 4730–4737.
[15] M.S. Khan, G.R. Pasha, and A.H. Pasha, Theoretical analysis of inverse Weibull distribution, WSEAS Trans. Math. 7 (2008) 30–38.
[16] S.J. Sanjay Kumar Singh, U. Umesh Singh and D. Kumar, Bayesian estimation of parameters of inverse Weibull distribution, J. Appl. Stat. 40 (2013) 1597–1607.
[17] D.V. Lindley and A.F. Smith, Bayes estimation for the linear model, J. R. Stat. Soc. Series B Stat. Methodol. 34 (1972) 141.
[18] D.N.P. Murthy, M. Xie and R. Jiang, Weibull Models, Wiley, New York, 2004.
[19] W. Nelson, Applied Lifetime Data Analysis, Wiley, New York, 1982.
[20] S. Shafiei, S. Darijani and H. Saboori, InverseWeibull power series distributions: properties and applications, J. Stat. Comput. Simul. 86 (2016) 1069–1094.
[21] S.M. Taheri, and R. Zarei, Bayesian system reliability assessment under the vague environment, Appl. Soft Comput. 11 (2011) 1614–1622.
[22] H.R. Varian, A Bayesian approach to real estate assessment, S.E. Fienberg and A. Zellner (eds.) Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage. North-Holland: Amsterdam, (1975) 195-208.
[23] W.H.E. Von Alven, Reliability Engineering by ARINC, Prentice Hall, Englewood Cliffs, New Jersey, 1964.
[24] J. Wang, D. Li and D. Chen, E-Bayesian Estimation and Hierarchical Bayesian Estimation of the System Reliability Parameter, Syst. Eng. Proc. 3 (2012) 282-289.
[25] F. Yousefzadeh, E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function, Commun. Stat. Theory Meth. 46 (2017) 1–8.
[26] S.S. Yaghoobzadeh, Estimating E-bayesian and hierarchical Bayesian of the scalar parameter of Gompertz distribution under type II censoring schemes based on fuzzy data, Commun. Stat. Theory Meth. 48 (2019) 831–840.
[27] R. Zarei, M. Amini, S.M. Taheri, and A.H. Rezaei, Bayesian estimation based on vague lifetime data, Soft Comput. 16 (2012) 165-174.
Volume 12, Issue 1
May 2021
Pages 461-471
  • Receive Date: 12 May 2020
  • Revise Date: 19 January 2021
  • Accept Date: 02 February 2021