153
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Statistical inference in Burr type XII lifetime model based on progressive randomly censored data

, , &

References

  • Abdel-Ghaly, A., G. Al-Dayian, and F. Al-Kashkari. 1997. The use of Burr type-XII distribution on software reliability growth modelling. Microelectronics Reliability 37 (2):305–13. doi: 10.1016/0026-2714(95)00124-7.
  • Abdel-Hamid, A. H. 2009. Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring. Computational Statistics & Data Analysis 53 (7):2511–23. doi: 10.1016/j.csda.2009.01.018.
  • Al-Duais, F. S. 2022. Bayesian reliability analysis based on the Weibull model under weighted general entropy loss function. Alexandria Engineering Journal 61 (1):247–55. doi: 10.1016/j.aej.2021.04.086.
  • Alam, I., and A. Ahmed. 2022. Inference on maintenance service policy under step-stress partially accelerated life tests using progressive censoring. Journal of Statistical Computation and Simulation 92 (4):813–29. doi: 10.1080/00949655.2021.1975282.
  • Aslam, M., M. Azam, and C.-H. Jun. 2016. Multiple dependent state repetitive group sampling plan for Burr XII distribution. Quality Engineering 28 (2):231–7. doi: 10.1080/08982112.2015.1068331.
  • Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring: Theory, methods, and applications. Boston: Birkhaüser Publisher.
  • Balakrishnan, N., and E. Cramer. 2014. The art of progressive censoring. New York: Birkhaüser.
  • Burr, I. W. 1942. Cumulative frequency functions. The annals of mathematical statistics 13 (2):215–32. doi: 10.1214/aoms/1177731607.
  • Chen, M. H., and Q. Shao. 1999. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8 (1):69–92.
  • Danish, M. Y., and M. Aslam. 2014. Bayesian analysis of randomly censored Burr Type XII distribution under different loss functions. Electronic Journal of Applied Statistical Analysis 7 (2):326–42.
  • Du, Y., and W. Gui. 2022. Statistical inference of Burr-XII distribution under adaptive type II progressive censored schemes with competing risks. Results in Mathematics 77 (2):81. doi: 10.1007/s00025-022-01617-4.
  • Fleming, T. R., and D. P. Harrington. 1991. Counting processes and survival analysis. Hoboken, NJ: John Wiley & Sons.
  • Friesl, M., and J. Hurt. 2007. On Bayesian estimation in an exponential distribution under random censorship. Kybernetika 43 (1):45–60.
  • Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. New York: Chapman and Hall/CRC.
  • Goel, N., and H. Krishna. 2022. Different methods of estimation in two parameter geometric distribution with randomly censored data. International Journal of System Assurance Engineering and Management 13 (4):1652–65. doi: 10.1007/s13198-021-01520-1.
  • Goel, R., and H. Krishna. 2020. Progressive type-II random censoring scheme with Lindley failure and censoring time distributions. International Journal of Agricultural and Statistical Sciences 16 (1):23–34.
  • Gupta, P. L., R. C. Gupta, and S. J. Lvin. 1996. Analysis of failure time data by Burr distribution. Communications in Statistics - Theory and Methods 25 (9):2013–24. doi: 10.1080/03610929608831817.
  • Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1):97–109. doi: 10.1093/biomet/57.1.97.
  • Herd, G. R. 1956. Estimation of the parameters of a population from a multi-censored sample. Ames, Iowa: Iowa State University.
  • Kayal, T., Y. M. Tripathi, D. P. Singh, and M. K. Rastogi. 2017. Estimation and prediction for Chen distribution with bathtub shape under progressive censoring. Journal of Statistical Computation and Simulation 87 (2):348–66. doi: 10.1080/00949655.2016.1209199.
  • Kohansal, A. 2020. Bayesian and classical estimation of R = P(X<Y) based on Burr type XII distribution under hybrid progressive censored samples. Communications in Statistics–Theory and Methods 49 (5):1043–81. doi: 10.1080/03610926.2018.1554126.
  • Koziol, J. A., and S. B. Green. 1976. A Cramer-Von Mises statistic for randomly censored data. Biometrika 63 (3):465–74.
  • Krishna, H., K. Kumar, and Vivekanand. (2015). Estimation in Maxwell distribution with randomly censored data. Journal of Statistical Computation and Simulation, 85(17):3560–3578. doi: 10.1080/00949655.2014.986483.
  • Kumar, I., and K. Kumar. 2022. On estimation of P(V<U) for inverse Pareto distribution under progressively censored data. International Journal of System Assurance Engineering and Management 13 (1):189–202.
  • Kumar, K., R. Garg, and H. Krishna. 2017. Nakagami distribution as a reliability model under progressive censoring. International Journal of System Assurance Engineering and Management 8 (1):109–22. doi: 10.1007/s13198-016-0494-3.
  • Kumar, K., and I. Kumar. 2020. Parameter estimation for inverse Pareto distribution with randomly censored life time data. International Journal of Agricultural and Statistical Sciences 16 (1):419–30.
  • Liang, T., L.-S. Chen, and M.-C. Yang. 2012. Efficient Bayesian sampling plans for exponential distributions with random censoring. Journal of Statistical Planning and Inference 142 (2):537–51. doi: 10.1016/j.jspi.2011.08.011.
  • Lio, Y., and T.-R. Tsai. 2012. Estimation of δ=P(X<Y) for Burr XII distribution based on the progressively first failure-censored samples. Journal of Applied Statistics 39 (2):309–22. doi: 10.1080/02664763.2011.586684.
  • Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. Equation of state calculations by fast computing machines. The Journal of Chemical Physics 21 (6):1087–92. doi: 10.1063/1.1699114.
  • Moore, D., and A. S. Papadopoulos. 2000. The Burr Type-XII distribution as a failure model under various loss functions. Microelectronics Reliability 40 (12):2117–22. doi: 10.1016/S0026-2714(00)00031-7.
  • Ng, H. K. T., P. S. Chan, and N. Balakrishnan. 2004. Optimal progressive censoring plans for the Weibull distribution. Technometrics 46 (4):470–81. doi: 10.1198/004017004000000482.
  • Ng, H. K. T., İ. Kınacı, C. Kuş, and P. S. Chan. 2017. Optimal experimental plan for multi-level stress testing with weibull regression under progressive type-ii extremal censoring. Communications in Statistics - Simulation and Computation 46 (4):2611–37. doi: 10.1080/03610918.2015.1054939.
  • Polosin, V. G., A. N. Mitroshin, and S. I. Gerashchenko. 2023. Burr type XII distribution in traffic control systems. Transportation Research Procedia 68:433–40. doi: 10.1016/j.trpro.2023.02.058.
  • Pradhan, B., and D. Kundu. 2009. On progressively censored generalized exponential distribution. TEST 18 (3):497–515. doi: 10.1007/s11749-008-0110-1.
  • Pradhan, B., and D. Kundu. 2013. Inference and optimal censoring schemes for progressively censored Birnbaum-Saunders distribution. Journal of Statistical Planning and Inference 143 (6):1098–108. doi: 10.1016/j.jspi.2012.11.007.
  • Ren, J., and W. Gui. 2021. Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution. Computational Statistics 36 (1):479–513. doi: 10.1007/s00180-020-01021-y.
  • Rodriguez, R. N. 1977. A guide to the Burr type XII distributions. Biometrika 64 (1):129–34. doi: 10.1093/biomet/64.1.129.
  • Saini, S., S. Tomer, and R. Garg. 2022. On the reliability estimation of multicomponent stress–strength model for Burr XII distribution using progressively first-failure censored samples. Journal of Statistical Computation and Simulation 92 (4):667–704. doi: 10.1080/00949655.2021.1970165.
  • Singh, B. 2013. Estimation of mean and its function using asymmetric loss function. International Journal of Soft Computing, Mathematics and Control (IJSCMC) 2 (1):27–44.
  • Soliman, A. A., A. H. Abd Ellah, N. A. Abou-Elheggag, and A. A. Modhesh. 2013. Estimation from Burr type XII distribution using progressive first-failure censored data. Journal of Statistical Computation and Simulation 83 (12):2270–90. doi: 10.1080/00949655.2012.690157.
  • Tierney, L., and J. B. Kadane. 1986. Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association 81 (393):82–6. doi: 10.1080/01621459.1986.10478240.
  • Wu, S.-J., Y.-J. Chen, and C.-T. Chang. 2007. Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution. Journal of Statistical Computation and Simulation 77 (1):19–27. doi: 10.1080/10629360600569204.
  • Xiaowen, D., J. Libin, T. Yuzhu, T. Maozai, and T. Manlai. 2020. Quantile regression for panel data models with fixed effects under random censoring. Communications in Statistics - Theory and Methods 49 (18):4430–45. doi: 10.1080/03610926.2019.1601221.
  • Zhang, Y.-Y. 2019. The Bayesian posterior estimators under six loss functions for unrestricted and restricted parameter spaces. In Bayesian Inference on complicated data, chapter 7, ed. Tang, N. Rijeka: IntechOpen.
  • Zimmer, W. J., J. B. Keats, and F. Wang. 1998. The Burr XII distribution in reliability analysis. Journal of Quality Technology 30 (4):386–94. doi: 10.1080/00224065.1998.11979874.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.