Bayesian parameter estimation of beta log Weibull distribution under Type II progressive censoring

References

• Balakrishnan, N. & Aggarwalla, R. Progressive Censoring: Theory, Methods and Applications. Birkhauser, Boston, c2000, USA (2000).
   Google Scholar
• Balakrishnan, N. & Hossain, A. Inference for the Type II Generalized Logistic Distribution under Progressive Type II Censoring. Journal of Statistical Computation and Simulation, 77(12), 1013-1031 (2007). doi: 10.1080/10629360600879876
   Web of Science ®Google Scholar
• Carpenter, J. and Bithell, J. Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. Statistics in medicine 19,1141-1164 (2000). doi: 10.1002/(SICI)1097-0258(20000515)19:9<1141::AID-SIM479>3.0.CO;2-F
   PubMed Web of Science ®Google Scholar
• Carrasco, J. M. F., Ortega, E. M. M. & Cordeiro, G. M. A Generalized Modified Weibull Distribution for Lifetime Modeling. Computational Statistics and Data Analysis, 53, 450-462 (2008). doi: 10.1016/j.csda.2008.08.023
   Web of Science ®Google Scholar
• Chen Z. A. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics and Probability Letters, 49, 155-61 (2000). doi: 10.1016/S0167-7152(00)00044-4
   Web of Science ®Google Scholar
• Cordeiro, G. M., Silva, G. O. & Ortega, E. M. M. The Beta Extended Weibull Family. Journal of Probability & Statistical Science, 10(10), 15-40 (2012).
   Google Scholar
• Cohen, A. C. & Norgaard, N. J. Progressively Censored Sampling in the three Parameter Gamma Distribution. Technometrics, 19, 333–340 (1977). doi: 10.1080/00401706.1977.10489556
   Web of Science ®Google Scholar
• Cohen, A. C. Progressively Censored Samples in Life Testing. Technometrics, 5, 327–339 (1963). doi: 10.1080/00401706.1963.10490102
   Web of Science ®Google Scholar
• Davis, H. T. & Feldstein, M. L. The Generalized Pareto law as a Model for Progressively Censored Survival Data. Biometrika, 66, 299–306 (1979). doi: 10.1093/biomet/66.2.299
   Web of Science ®Google Scholar
• Efron, B. The Jackknife, the Bootstrap and other Resampling Plans. CBMS - NSF Regional Conference Series in Applied Mathematics. No. 38, Philadelphia (PA): SIAM (1982).
   Google Scholar
• Flaih, A., Elsalloukh, H., Mendi, E. & Milanova, M. The Exponentiated Inverted Weibull Distribution. Applied Mathematics Information Science, 6(2), 167-171 (2012).
   Google Scholar
• Gelfand, A. E. & Smith, A. F. Sampling Based Approaches to Calculating Marginal Densities. Journal of American Statistical Association, 85(410), 398-409 (1990). doi: 10.1080/01621459.1990.10476213
   Web of Science ®Google Scholar
• Green, E. J., Roesh, F. A. Jr., Smith, A. F. M. & Strawderman, W. E. Bayes Estimation for the Three Parameters Weibull Distribution with Tree Diameters Data. Biometrics, 50(4), 254-269 (1994). doi: 10.2307/2533217
   Google Scholar
• Hall, P. Theoretical Comparison of Bootstrap Confidence Intervals. Annals of Statistics, 16, 927-953 (1988). doi: 10.1214/aos/1176350933
   Web of Science ®Google Scholar
• Hastings, W. Monte Carlo Sampling Methods using Markov Chains and their Applications. Biometrika, 55, 97–109 (1970). doi: 10.1093/biomet/57.1.97
   Google Scholar
• Hossain, A. M. & Zimmer, W. J. Comparisons of Estimation Methods for Weibull Parameters: Complete and Censored Samples. Journal of Statistical Computation and Simulation, 73(2), 145-153 (2003). doi: 10.1080/00949650215730
   Web of Science ®Google Scholar
• Johnson, N. L., Kotz, S. & Balakrishnan, N. Continuous Univariate Distributions. 2nd edition. Wiley, New York. 1 (1994).
   Google Scholar
• Lawless, J. F. Statistical Models and Methods for Lifetime Data. 2nd ed., John Wiley and Sons, New York, USA (2003).
   Google Scholar
• Lindley, D. V. Approximate Bayesian Method. Trabajos de Estadistica, 31, 223-237 (1980). doi: 10.1007/BF02888353
   Google Scholar
• Meeker, W. Q and Escobar, L. A. Statistical Methods for Reliability Data. Wiley, New York (1998).
   Google Scholar
• Nicholas, M. D. & Padgett, W. J. A Bootstrap Control Chart for Weibull Percentiles. Quality and Reliability Engineering International, 22(2), 141-151 (2006). doi: 10.1002/qre.691
   Web of Science ®Google Scholar
• Ortega, E. M. M., Cordeiro, G. M. & Kattan, M. W. The Log-Beta Weibull Regression Model with Application to Predict Recurrence of Prostate Cancer. Statistical Papers, 54(1), 113-132 (2013). doi: 10.1007/s00362-011-0414-1
   Web of Science ®Google Scholar
• Rastogi, M. K, Tripathi, Y. M. & Wu. S. J. Estimating the Parameters of a Bathtub-Shaped Distribution under Progressive Type II Censoring. Journal Applied Statistics, 39(11), 2389-2411 (2012). doi: 10.1080/02664763.2012.710899
   Web of Science ®Google Scholar
• Shamilov, A., Usta, I. & Kantar, Y. M. The Distribution of Minimizing Maximum Entropy: Alternative to Weibull Distribution for Wind Speed. WSEAS Transactions on Mathematics, 5(6), 695-700 (2006).
   Google Scholar
• Singh P. K., Singh S. K. & Singh U. Bayes Estimator of Inverse Gaussian Parameters under General Entropy Loss Function Using Lindley’s Approximation. Communication in Statistics-Simulation and Computation, 37(9), 1750–1762 (2008). doi: 10.1080/03610910701884054
   Web of Science ®Google Scholar
• Singh, R., Singh, S. K., Singh, U. & Singh, G. P. Bayes Estimator of Generalized Exponential Parameters under General Entropy Loss Function using Lindley’s Approximation. Statistics in transition-new series, 10, 109-127 (2009).
   Google Scholar
• Singh, S. K, Singh, U. & Sharma, V. K. Expected Total Test time and Bayesian Estimation for Generalized Lindley Distribution under Progressive Type-II censored sample where Removals follows the Beta-binomial Probability Law. Applied Mathematics and Computation, Elsevier, 222, 402-419 (2013).
   Google Scholar
• Tahir, M. H., Cordeiro, G. M., Mansoor, M. & Zubair M. The Weibull-Lomax Distribution: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 44(2), 461-480 (2015).
   Web of Science ®Google Scholar
• Tierney, L. Markov chains for exploring posterior distributions. The Annals of Statistics, 22(4), 1701-1786 (1994). doi: 10.1214/aos/1176325750
   Web of Science ®Google Scholar
• Upadhyay, S. K. & Gupta, A. A Bayes Analysis of Modified Weibull distribution via Markov chain Monte Carlo Simulation. Journal of Statistical Computation and Simulation, 80(3), 241-254 (2010). doi: 10.1080/00949650802600730
   Web of Science ®Google Scholar
• White, J. S. The Moments of Log-Weibull Order Statistics. Technimetrics, 11(2), 373-386 (1969). doi: 10.1080/00401706.1969.10490691
   Web of Science ®Google Scholar
• Xie, M., Tang, Y. and Goh, T. N. A modified Weibull extension with bathtub failure rate function. Reliability Engineering and System Safety, 76, 279-285 (2002). doi: 10.1016/S0951-8320(02)00022-4
   Web of Science ®Google Scholar
• Zaharim, A., Najid, S. K., Razali, A. M. & Sopian, K. The Suitability of Statistical Distribution in Fitting Wind Speed Data. WSEAS Transactions on Mathematics, 7(12), 718-727 (2008).
   Google Scholar