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J. Math. and Appl. 2021, 1(1): 1-11 Back to browse issues page
Bayesian estimation of the parameters for two-parameter bathtub-shaped lifetime distribution based on ranked set sampling
Mehdi Basikhasteh1, Fazlollah Lak *1, Mahmoud Afshari1
1- Department of Statistics, Faculty of Sciences, Persian Gulf University, Bushehr 75169, Iran.
Abstract:   (1375 Views)

Keywords: Bayesian estimation, Monte Carlo Markov chain, ranked set sampling, two-parameter bathtub-shaped lifetime distribution.
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Type of Study: Research | Subject: General algebraic systems
Received: 2020/12/28 | Accepted: 2021/01/1 | ePublished: 2021/01/1
1. A.M. Sarhan, D.C. Hamilton, B. Smith, Parameter estimation for a two-parameter bathtub-shaped lifetime distribution, Appl. Math. Modeling, 36 (2012) 5380-5392.
2. D. Ardia, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag Berlin Heidelberg, 2008.
3. B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A First Course in Order Statistics, John Wiley$And$Sons, New York, 1992.
4. M.H. Chen, Q.M. Shao, Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comp. and Graphical Statistics, 8 (1999) 69-92.
5. Z. Chen, A new two- parameter lifetime distribution with bathtub shape or increasing failure rate function, Stat. and Probabil. Letters, 49 (2000) 155-161.
6. A.E. Gelfand, A.F.M. Smith, Sampling-based approaches to calculating marginal densities, J. Amer. Stat. Assoc., 85 (1990) 398-409.
7. W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57 (2003) 97-109.
8. U. Hjorth, A reliability distribution with increasing, decreasing, and bathtub-shaped failure rate, Technometrics, 22 (1980) 99-107.
9. J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 2003.
10. J.-W. Wu, H.-L. Lu, C.-H. Chen, C.-H. Wu. Statistical inference about the shape parameter of the new two-parameter bathtub-shaped lifetime distribution, Qual. Reliab. Eng. Int., 20 (2004) 607-616.
11. P.H. Kvam, F.J. Samaniego, Non-parametric maximum likelihood estimation based on ranked set sampling, J. Amer. Stat. Assoc., 89 (1994) 526-537.
12. M. Lavine, The Bayesics of ranked set sampling, J. Environ. Ecol. Stat., 6 (1999) 47-57.
13. L. M. Leemis, Lifetime distribution identities, IEEE Transactions on Reliability, 35(2) (1986) 170-174.
14. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equations of state calculations by fast computing
15. machines, J. Chem. Phys., 21 (1953) 1087-1091.
16. G.~A. McIntyre, A method for unbiased selective sampling using ranked sets, Aust. J. of Agricultural Research, 3(4) (1952) 385--390.
17. H.A. Muttlak, W. Al-Sabah, Statistical quality control using ranked set sampling, J. Appl. Stat., 30 (2003) 1055-1078.
18. G. Mudholkar, A method for unbiased selective sampling using ranked set, Aust. J. Agri. Res., 3 (1952) 385-390.
19. G. S. Mudholkar, D. K. Srivastava, Exponentiated Weibull family for analysing bathtub failure rate data, IEEE Transactions on Reliability, 42(2)} (1993) 299-302.
20. G.P. Patil, A.K. Sinha, C. Taillie, Relative precision of ranked set sampling: a comparison with the regression estimator, Environmetrics, 4 (1993) 399-412.
21. C. Robert, G. Casella, Monte Carlo Statistical Methods, Springer Text in Statistics, 2004.
22. G. Roberts, A. Smith, Simple Conditions for the Convergence of the Gibbs Sampler and Metropolis-Hastings Algorithm, Stochastic Processes and their Applications, 49(2) (1994) 207-216.
23. A. Sadek, F. Alharbi, Weibull-Bayesian analysis based on ranked set sampling, Int. J. Adv. Stat. Probab., 2 (2014) 114-123.
24. A. Sadek, K.S. Sultan, N. Balakrishnan, Bayesian estimation based on ranked set sampling using asymmetric loss function, Bull. Malays. Math. Sci. Soci., 38 (2015) 707-718.
25. S.-J. Wu. Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring, J. Appl. Stat., 35(10) (2008) 1139-1150.
26. R. M. Smith, L. J. Bain, An exponential power life-testing distribution, Communications in Statistics - Theory and Methods, 4 (1975) 469-481.
27. K. Takahasi, K. Wakimoto, On unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Stat. Math., 20 (1968) 1-31.

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Basikhasteh M, Lak F, Afshari M. Bayesian estimation of the parameters for two-parameter bathtub-shaped lifetime distribution based on ranked set sampling. J. Math. and Appl.. 2021; 1 (1) :1-11
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مجله ریاضیات و کاربردها Journal of Mathematics and Applications
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