References
- Barndorff-Nielsen, O. E. 1986. Inference on full or partial parameters based on the standardized signed log likelihood ratio. Biometrika 73 (2):307–22. doi:10.2307/2336207.
- Barndorff-Nielsen, O. E. 1991. Modified signed log likelihood ratio. Biometrika 78 (3):557–63. doi:10.1093/biomet/78.3.557.
- Barndorff-Nielsen, O. E., and D. R. Cox. 1994. Inference and asymptotics. London: Chapman and Hall.
- Calabria, R., M. Guida, and G. Pulcini. 1988. Some modified maximum likelihood estimators for the Weibull process. Reliability Engineering & System Safety 23 (1):51–58. doi:10.1016/0951-8320(88)90027-0.
- Chumnaul, J., and M. Sepehrifar. 2018. Generalized confidence interval for the scale parameter of the power-law process with incomplete failure data. Computational Statistics & Data Analysis 128:17–33. doi:10.1016/j.csda.2018.06.007.
- Cocozza-Thivent, C. 1997. Processus stochastiques et abilite des systemes. Berlin: Springer-Verlag.
- Cox, D. R., and D. V. Hinkley. 1974. Theoretical statistics. London: Chapman and Hall.
- Crow, L. H. 1975. Reliability analysis for complex, repairable systems. AMSAA Technical Report No. 138. Maryland: Aberdeen Proving Ground.
- Crow, L. H. 1982. Confidence interval procedures for the Weibull process with application to reliability growth. Technometrics 24 (1):67–72. doi:10.1080/00401706.1982.10487711.
- DiCiccio, T. J., and M. A. Martin. 1993. Simple modifications for signed roots of likelihood ratio statistics. Journal of the Royal Statistical Society: Series B (Methodological) 55 (1):305–16. doi:10.1111/j.2517-6161.1993.tb01485.x.
- DiCiccio, T. J., M. A. Martin, and S. E. Stern. 2001. Simple and accurate one-sided inference from signed roots of likelihood ratios. Canadian Journal of Statistics 29 (1):67–76. doi:10.2307/3316051.
- Duane, J. T. 1964. Learning curve approach to reliability monitoring. IEEE Transactions on Aerospace 2 (2):563–66. doi:10.1109/TA.1964.4319640.
- Engelhardt, M., and L. J. Bain. 1978. Prediction intervals for the Weibull process. Technometrics 20 (2):167–69. doi:10.1080/00401706.1978.10489642.
- Engelhardt, M., and L. J. Bain. 1992. Statistical analysis of a Weibull process with left censored data. In Survival analysis: State of the art (Columbus, OH, 1991), volume 211 of NATO Advanced Science Institutes Series E: Applied Sciences, 173–95. Dordrecht: Kluwer Academic Publishers.
- Finklestein, J. M. 1976. Confidence bounds on the parameters of the Weibull process. Technometrics 18:115–17.
- Fraser, D. A. S., N. Reid, and J. Wu. 1999. A simple general formula for tail probabilities for frequentist and Bayesian inference. Biometrika 86 (2):249–64. doi:10.1093/biomet/86.2.249.
- Gaudoin, O., B. Yang, and M. Xie. 2006. Confidence intervals for the scale parameter of the power-law process. Communications in Statistics - Theory and Methods 35 (8):1525–38. doi:10.1080/03610920600637412.
- Guida, M., R. Calabria, and G. Pulcini. 1989. Bayes inference for a non-homogeneous Poisson process with power law intensity. IEEE Transactions on Reliability 38 (5):603–609. doi:10.1109/24.46489.
- Higgins, J. J., and C. P. Tsokos. 1981. A quasi-Bayes estimate of the failure intensity of a reliability growth model. IEEE Transactions on Reliability 30 (5):471–75. doi:10.1109/TR.1981.5221176.
- Huang, Y., and V. Bier. 1998. A natural conjugate prior for the non-homogeneous Poisson process with a power law intensity function. Communications in Statistics - Simulation and Computation 27 (2):525–51. doi:10.1080/03610919808813493.
- Kyparisis, J., and N. D. Singpurwalla. 1985. Bayesian inference for the Weibull process with applications to assessing software reliability growth and predicting software failures. In Computer Science and Statistics: Proceedings of the Sixteenth Symposium on the Interface, ed. L. Billard. Amsterdam, 57–64.
- Lee, L., and S. K. Lee. 1978. Some results on inference for the Weibull process. Technometrics 20 (1):41–45. doi:10.1080/00401706.1978.10489616.
- Ni, W., K. Paul, and L. Jye-Chyi. 2007. Detection and estimation of a mixture in power law processes for a repairable system. Journal of Quality Technology 39:140–50.
- Pierce, D. A., and D. Peters. 1992. Practical use of higher order asymptotics for multiparameter exponential families. Journal of the Royal Statistical Society: Series B (Methodological) 54 (3):701–37. doi:10.1111/j.2517-6161.1992.tb01445.x.
- Rigdon, S. E., and A. P. Basu. 1989. The power law process: A model for the reliability of repairable systems. Journal of Quality Technology 21 (4):251–60. doi:10.1080/00224065.1989.11979183.
- Rigdon, S. E., and A. P. Basu. 1990. Estimating the intensity function of a power law process at the current time: Time truncated case. Communications in Statistics - Simulation and Computation 19 (3):1079–104. doi:10.1080/03610919008812906.
- Ryan, K. J. 2003. Some flexible families of intensities for non-homogeneous Poisson process models and their Bayes inference. Quality and Reliability Engineering International 19 (2):171–81. doi:10.1002/qre.520.
- Skovgaard, I. M. 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28 (1):3–32. doi:10.1111/1467-9469.00223.
- Switamy, A. P., A. Sutarman, and D. S. Open. 2017. Maximum likelihood based on Newton Raphson, fisher scoring and expectation maximization algorithm application on accident data. International Journal of Advanced Research 6:965–69.
- Tian, G. L., M. L. Tang, and J. W. Yu. 2021. Bayesian estimation and prediction for the power law process with left-truncated data. Journal of Data Science 9 (3):445–70. doi:10.6339/JDS.201107_09(3).0009.
- Wang, B. X., M. Xie, and J. X. Zhou. 2013. Generalized confidence interval for the scale parameter of the power-law process. Communications in Statistics - Theory and Methods 42 (5):898–906. doi:10.1080/03610926.2011.588363.
- Yu, J. W., G. L. Tian, and M. L. Tang. 2008. Statistical inference and prediction for the Weibull process with incomplete observations. Computational Statistics & Data Analysis 52 (3):1587–603. doi:10.1016/j.csda.2007.05.003.