Properties of k-record posteriors for the Weibull model

References

• Arnold, B. C., Balakrishnan, N., & Nagaraja, H. N. (2011). Records. John Wiley & Sons.
   Google Scholar
• Balakrishnan, N., Balasubramanian, K., & Panchapakesan, S. (1996). δ-exceedance records. Journal of Applied Statistical Science, 4(2/3), 123–132.
   Google Scholar
• Benestad, R. E. (2003). How often can we expect a record event? Climate Research, 25(1), 3–13. https://doi.org/10.3354/cr025003
   Web of Science ®Google Scholar
• Berger, J. O., Bernardo, J. M., & Sun, D. (2015). Overall objective priors. Bayesian Analysis, 10(1), 189–221.
   Web of Science ®Google Scholar
• Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference. Journal of the Royal Statistical Society: Series B (Methodological), 41(2), 113–128.
   Web of Science ®Google Scholar
• Bernardo, J. M. (2005). Reference analysis. Handbook of Statistics, 25, 17–90. https://doi.org/10.1016/S0169-7161(05)25002-2
   Google Scholar
• Chandler, K. N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society: Series B (Methodological), 14(2), 220–228.
   Web of Science ®Google Scholar
• Doostparast, M. (2011). Goodness-of-fit tests for Weibull populations on the basis of records. arXiv:1110.5509.
   Google Scholar
• Dziubdziela, W., & Kopociński, B. (1976). Limiting properties of the kth record values. Applicationes Mathematicae, 15(2), 187–190. https://doi.org/10.4064/am-15-2-187-190
   Google Scholar
• Empacher, C., Kamps, U., & Volovskiy, G. (2023). Statistical prediction of future sports records based on record values. Stats, 6(1), 131–147. https://doi.org/10.3390/stats6010008
   Google Scholar
• Gembris, D., Taylor, J. G., & Suter, D. (2007). Evolution of athletic records: Statistical effects versus real improvements. Journal of Applied Statistics, 34(5), 529–545. https://doi.org/10.1080/02664760701234850
   Web of Science ®Google Scholar
• Glick, N. (1978). Breaking records and breaking boards. The American Mathematical Monthly, 85(1), 2–26. https://doi.org/10.1080/00029890.1978.11994501
   Web of Science ®Google Scholar
• Gugushvili, S., & Spreij, P. (2014). Nonparametric Bayesian drift estimation for multidimensional stochastic differential equations. Lithuanian Mathematical Journal, 54(2), 127–141. https://doi.org/10.1007/s10986-014-9232-1
   Web of Science ®Google Scholar
• Hassan, A. S., Nagy, H. F., Muhammed, H. Z., & Saad, M. S. (2020). Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values. Journal of Taibah University for Science, 14(1), 244–253. https://doi.org/10.1080/16583655.2020.1721751
   Web of Science ®Google Scholar
• Jafari, A. A., & Bafekri, S. (2021). Inferences on the performance index of Weibull distribution based on k-record values. Journal of Computational and Applied Mathematics, 382, 113060. https://doi.org/10.1016/j.cam.2020.113060
   Web of Science ®Google Scholar
• Juhás, M., & Skřivánková, V. (2014). Characterization of general classes of distributions based on independent property of transformed record values. Applied Mathematics and Computation 226 44–50. https://doi.org/10.1016/j.amc.2013.10.037
   Web of Science ®Google Scholar
• Kang, S. G., Lee, W. D., & Kim, Y. (2017). Noninformative priors for the ratio of the shape parameters of two Weibull distributions. Computational Statistics, 32(1), 35–50. https://doi.org/10.1007/s00180-015-0631-5
   Web of Science ®Google Scholar
• Kass, R. E., & Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91(435), 1343–1370. https://doi.org/10.1080/01621459.1996.10477003
   Web of Science ®Google Scholar
• Kauffman, S., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology, 128(1), 11–45. https://doi.org/10.1016/S0022-5193(87)80029-2
   PubMed Web of Science ®Google Scholar
• Kim, Y., & Seo, J. I. (2020). Objective Bayesian prediction of future record statistics based on the exponentiated Gumbel distribution: Comparison with time-series prediction. Symmetry, 12(9), 1443. https://doi.org/10.3390/sym12091443
   Google Scholar
• Kizilaslan, F., & Nadar, M. (2017). Statistical inference of P(X<Y) for the Burr Type XII distribution based on records. Hacettepe Journal of Mathematics and Statistics, 46(4), 713–742.
   Web of Science ®Google Scholar
• Lee, W. D., Kang, S. G., & Kim, Y. (2015). Noninformative priors for the common shape parameters of Weibull distributions. Journal of the Korean Statistical Society, 44(4), 668–679. https://doi.org/10.1016/j.jkss.2015.07.003
   Web of Science ®Google Scholar
• Lee, W. D., Kang, S. G., & Kim, Y. (2017). Objective Bayesian inference for the ratio of the scale parameters of two Weibull distributions. Communications in Statistics-Theory and Methods, 46(10), 4943–4956. https://doi.org/10.1080/03610926.2015.1091477
   Web of Science ®Google Scholar
• Liang, F., Paulo, R., Molina, G., Clyde, M. A., & Berger, J. O. (2008). Mixtures of g priors for Bayesian variable selection. Journal of the American Statistical Association, 103(481), 410–423. https://doi.org/10.1198/016214507000001337
   Web of Science ®Google Scholar
• Madadi, M., & Tata, M. (2014). Shannon information in k-records. Communications in Statistics–Theory and Methods, 43(15), 3286–3301. https://doi.org/10.1080/03610926.2012.697965
   Web of Science ®Google Scholar
• Martinez, E. Z., de Freitas, B. C. L., Achcar, J. A., Aragon, D. C., & de Oliveira Peres, M. V. (2022). Exponentiated Weibull models applied to medical data in presence of right-censoring, cure fraction and covariates. Statistics, Optimization & Information Computing, 10(2), 548–571. https://doi.org/10.19139/soic.v10i2
   Google Scholar
• Nasiri, P., & Hosseini, S. (2012). Statistical inferences for Lomax distribution based on record values (Bayesian and classical). Journal of Modern Applied Statistical Methods, 11(1), 179–189. https://doi.org/10.22237/jmasm/1335845640
   Google Scholar
• Neal, P., & Roberts, G. (2008). Optimal scaling for random walk Metropolis on spherically constrained target densities. Methodology and Computing in Applied Probability, 10(2), 277–297. https://doi.org/10.1007/s11009-007-9046-2
   Web of Science ®Google Scholar
• Nevzorov, V. B. (2000). Records: Mathematical Theory. Providence: AMS.
   Google Scholar
• Northrop, P. J., & Attalides, N. (2016). Posterior propriety in Bayesian extreme value analyses using reference priors. Statistica Sinica, 26(2), 721–743.
   Web of Science ®Google Scholar
• R Core Team (2024). R: A Language and Environment for Statistical Computing Reference. Vienna: R Foundation for Statistical Computing.
   Google Scholar
• Ramos, E., Egbon, O. A., Ramos, P. L., Rodrigues, F. A., & Louzada, F. (2020). Objective Bayesian analysis for the differential entropy of the Gamma distribution. arXiv:2012.14081.
   Google Scholar
• Ramos, E., Ramos, P. L., & Louzada, F. (2020). Posterior properties of the Weibull distribution for censored data. Statistics & Probability Letters, 166, 108873. https://doi.org/10.1016/j.spl.2020.108873
   Web of Science ®Google Scholar
• Ramos, P. L., Achcar, J. A., Moala, F. A., Ramos, E., & Louzada, F. (2017). Bayesian analysis of the generalized gamma distribution using non-informative priors. Statistics, 51(4), 824–843.
   Web of Science ®Google Scholar
• Ramos, P. L., Almeida, M. H., Louzada, F., Flores, E., & Moala, F. A. (2022). Objective Bayesian inference for the Capability index of the Weibull distribution and its generalization. Computers & Industrial Engineering, 167, 108012. https://doi.org/10.1016/j.cie.2022.108012
   Web of Science ®Google Scholar
• Ramos, P. L., Dey, D. K., Louzada, F., & Ramos, E. (2021). On posterior properties of the two parameter gamma family of distributions. Anais da Academia Brasileira de Ciencias, 93(suppl 3), e20190826. https://doi.org/10.1590/0001-3765202120190826
   PubMedGoogle Scholar
• Ramos, P. L., Rodrigues, F. A., Ramos, E., Dey, D. K., & Louzada, F. (2023). Power laws distributions in objective priors. Statistica Sinica, 33(3), 1–53.
   Web of Science ®Google Scholar
• Robert, C. P., & Casella, G. (2010). Introducing Monte Carlo Methods with R (Vol. 18). New York: Springer.
   Google Scholar
• Shakhatreh, M. K., Dey, S., & Alodat, M. T. (2021). Objective Bayesian analysis for the differential entropy of the Weibull distribution. Applied Mathematical Modelling, 89, 314–332. https://doi.org/10.1016/j.apm.2020.07.016
   Web of Science ®Google Scholar
• Shakhatreh, M. K., Lemonte, A. J., & Cordeiro, G. M. (2020). On the generalized extended exponential-Weibull distribution: Properties and different methods of estimation. International Journal of Computer Mathematics, 97(5), 1029–1057. https://doi.org/10.1080/00207160.2019.1605062
   Web of Science ®Google Scholar
• Sun, D. (1997). A note on noninformative priors for Weibull distributions. Journal of Statistical Planning and Inference, 61(2), 319–338. https://doi.org/10.1016/S0378-3758(96)00155-3
   Web of Science ®Google Scholar
• Syam, A. H., & Barakat, H. M. (2022). Information measures for record values and their concomitants under Haung-Kotz FGM bivariate distribution. Bulletin of Faculty of Science, Zagazig University, 2022(3), 122–130. https://doi.org/10.21608/bfszu.2022.147965.1154
   Google Scholar
• Teimouri, M., & Nadarajah, S. (2013). Bias corrected MLEs for the Weibull distribution based on records. Statistical Methodology, 13, 12–24. https://doi.org/10.1016/j.stamet.2013.01.001
   Web of Science ®Google Scholar
• Thornton, C., Hutter, F., Hoos, H. H., & Leyton-Brown, K. (2013). Auto-WEKA: Combined selection and hyperparameter optimization of classification algorithms. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 847–855).
   Google Scholar
• Vidović, Z. (2021). Random chord in a circle and Bertrand's paradox: New generation method, extreme behaviour and length moments. Bulletin of the Korean Mathematical Society, 58(2), 433–444.
   Web of Science ®Google Scholar
• Volovskiy, G., & Kamps, U. (2023). Likelihood-based prediction of future Weibull record values. REVSTAT-Statistical Journal, 21(3), 425–445.
   Web of Science ®Google Scholar
• Wang, B. X., & Ye, Z. S. (2015). Inference on the Weibull distribution based on record values. Computational Statistics & Data Analysis, 83, 26–36. https://doi.org/10.1016/j.csda.2014.09.005
   Web of Science ®Google Scholar
• Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18(3), 293–297. https://doi.org/10.1115/1.4010337
   Web of Science ®Google Scholar
• Wergen, G. (2013). Records in stochastic processes: Theory and applications. Journal of Physics A: Mathematical and Theoretical, 46(22), 223001. https://doi.org/10.1088/1751-8113/46/22/223001
   Web of Science ®Google Scholar
• Xia, Z. P., Yu, J. Y., Cheng, L. D., Liu, L. F., & Wang, W. M. (2009). Study on the breaking strength of jute fibres using modified Weibull distribution. Composites Part A: Applied Science and Manufacturing, 40(1), 54–59. https://doi.org/10.1016/j.compositesa.2008.10.001
   Web of Science ®Google Scholar
• Zellner, A. (1977). Maximal data information prior distributions. New Developments in the Applications of Bayesian Methods (pp. 211–232). North-Holland: Elsevier.
   Google Scholar