Likelihood Testing With Censored and Missing Duration Data

References

• Amstadter, B. L. 1971. Reliability mathematics, chap. 9. New York, NY: McGraw-Hill.
   Google Scholar
• Alvarez-Andradea, S., N. Balakrishnan, and L. Bordes. 2007. Homogeneity tests based on several progressively Type-II censored samples. J. Multivariate Anal., 98, 1195–1213.
   Web of Science ®Google Scholar
• Bahadur, R. R. 1965. An optimal property of the likelihood ratio statistic. In Proc. 5th Berkeley Symposium on Probability Theory and Mathematical Statistics, vol. 1, ed. L. Le Cam and J. Neyman, 13–26. Berkeley, CA: University of California Press.
   Google Scholar
• Bain, L. J., and M. Engelhardt. 1992. Introduction to probability and mathematical statistics (2nd ed.). Boston, MA: PWSKENT Publishing Company.
   Google Scholar
• Balakrishnan, N. 2007. Progressive censoring methodology: An appraisal. TEST, 16, 211–259.
   Web of Science ®Google Scholar
• Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring theory, methods, and applications, Series: Statistics for Industry and Technology, XV. Boston, MA: Birkhäuser.
   Google Scholar
• Balakrishnan, N., and R. A. Sandhu. 1996. Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type-II censored samples. Sankhya, Ser. B, 58, 1–9.
   Google Scholar
• Barndorf-Nielsen, O. E. 1978. Information and exponential families in statistical theory, 111–115. New York, NY: John Wiley Sons.
   Google Scholar
• Bartholomew, D. J. 1963. The sampling distribution of an estimate arising in life testing. Technometrics, 5, 361–374.
   Web of Science ®Google Scholar
• Childs, A., B. Chandrasekar, N. Balakrishnan, and D. Kundu. 2003. Exact likelihood inference based on Type I and Type II hybrid censored samples from the exponential distribution. Ann. Inst. Stat. Math., 55(2), 319–330.
   Web of Science ®Google Scholar
• Ciuperca, G. 2002. Likelihood ratio statistic for exponential mixtures. Ann. Inst. Stat. Math. 54(3), 585–594.
   Web of Science ®Google Scholar
• Cohen, A. C. 1991. Truncated and censored samples. Statistics, a Series of Textbooks and Monographs. New York, NY: Marcel Dekker.
   Google Scholar
• Coit, D. W., and T. Jin. 2000. Gamma distribution parameter estimation for field reliability data with missing failure times. IIE Trans. 32, 1161–1166.
   Web of Science ®Google Scholar
• Coit, D. W., and Dey. K. A. 1999. Analysis of grouped data from field-failure reporting systems. Reliability Eng. System Safety, 65, 95–101.
   Web of Science ®Google Scholar
• Cole, K. N., P. B. Nagarsenker, and B. N. Nagarsenker. 1987. A test for equality of exponential distributions based on Type-II censored samples. IEEE Trans. Reliability, 36(1), 94–97.
   Google Scholar
• Corless, R. M., G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth. 1996. On the Lambert W function. Adv. Comput. Math. 5, 329–359.
   Web of Science ®Google Scholar
• Corless, R. M., G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth. 1993. Lambert’s W function in Maple. Maple Tech. Newslett., 9, 12–22.
   Google Scholar
• Dey, K. A. 1982. Statistical analysis of noisy and incomplete failure data. In Proceedings Annual Reliability and Maintainability Symposium (RAMS), IEEE, Piscataway, NJ, 93–97.
   Google Scholar
• Economou, P., and M. Stehlík. 2014. On small samples testing for frailty through homogeneity test. Commun. Stat. Simul. Comput. http://dx.doi.org/10.1080/03610918.2013.763982.
   Google Scholar
• Epstein, B., and M. Sobel. 1954. Some theorems relevant to life testing from an exponential distribution. Ann. Math. Stat. 25, 373–381.
   Google Scholar
• Gaudoin, O., and J. L. Soler. 1992. Statistical analysis of the geometric de-eutrophication software reliability model. IEEE Trans. on Reliability, 41(4), 518–524.
   Web of Science ®Google Scholar
• Gautam, N. 1999. Erlang distribution: Description and case study. In Industrial engineering applications and practice: Users encyclopedia, eds. A. Mital and J. Chen.
   Google Scholar
• Hamada, M. S., A. G Wilson, C. S. Reese, and H. F. Martz. 2008. Bayesian reliability. Springer Series in Statistics. New York, NY: Springer.
   Google Scholar
• Johansen, S. 1979. Introduction to the theory of regular exponential families. Lecture Notes, vol. 3. Copenhagen, Denmark: Institute of Mathematical Statistics, University of Copenhagen.
   Google Scholar
• Kleinrock, L. 1975. Queueing systems, vol. 1, 71–72, 119–134. Toronto, Canada: John Wiley & Sons.
   Google Scholar
• Kundu, D., and A. Joarder. 2006. Analysis of Type-II progressively hybrid censored data. Comput. Stat. Data Anal. 50, 2509–2528.
   Web of Science ®Google Scholar
• Lehmann, E. L., and J. P. Romano. 2005. Testing statistical hypotheses. New York, NY: Springer-Verlag, LLC.
   Google Scholar
• Lin, D. K. J., J. S. Usher, and F. M. Guess. 1996. Bayes estimation of component from masked system-life data. IEEE Trans. Reliability, 45, 233–237.
   Web of Science ®Google Scholar
• Little, R. J. A., and D. B. Rubin. 1987. Statistical analysis with missing data. New York, NY: Wiley.
   Google Scholar
• Lomax, K. S. 1954. Business failures: Another example of the analysis of failure data. J. Am. Stat. Assoc. 49, 847–852.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 2007. Life distributions. New York, NY: Springer.
   Google Scholar
• Mosler, K., and L. Haferkamp. 2007. Size and power of recent tests for homogeneity in exponential mixtures. Commun. Stat. Simulation Comput. 36, 493–504.
   Web of Science ®Google Scholar
• Mosler, K., and C. Scheicher. 2008. Homogeneity testing in a Weibull mixture model. Stat. Papers, 49, 315–332.
   Web of Science ®Google Scholar
• Nagarsenker, P. B. 1980. On a test of equality of several exponential survival distributions. Biometrika, 67(2), 475–478.
   Web of Science ®Google Scholar
• Philbrick, S. W. 1985. A practical guide to the single parameter Pareto distribution. Proc. Casualty Actuarial Society, LXXII, 44–84.
   Google Scholar
• Rublík, F. 1989a. On optimality of the LR tests in the sense of exact slopes, Part 1, General case. Kybernetika, 25, 13–25.
   Web of Science ®Google Scholar
• Rublík, F. 1989b. On optimality of the LR tests in the sense of exact slopes, Part 2, Application to individual distributions. Kybernetika, 25, 117–135.
   Web of Science ®Google Scholar
• Soland, R. M. 1966. Use of Weibull distribution in Bayesian decision theory, Report No. RAC-TP-225. McLean, VA: Research Analysis Corporation.
   Google Scholar
• Soland, R. M. 1969. Bayesian analysis of the Weibull process with unknown scale and shape parameters. IEEE Trans. Reliability, 18(4), 181–184.
   Google Scholar
• Severini, T. A. 1999. On the relationship between Bayesian and non-Bayesian elimination of nuisance parameters. Stat. Sin. 9, 713–724.
   Web of Science ®Google Scholar
• Severini, T. A. 2006. Likelihood methods in statistics. Oxford Statistical Science Series. New York, NY: Oxford University Press.
   Google Scholar
• Severini, T. A. 2010. Likelihood ratio statistics based on an integrated likelihood. Biometrika, 97(2), 481–496.
   Web of Science ®Google Scholar
• Shoukri, M. M. 1987. Simple Bayes test of equality of exponential means. IEEE Trans. Reliability, 36(5), 613–616.
   Google Scholar
• Stehlík, M. 2003. Distributions of exact tests in the exponential family. Metrika, 57, 145–164.
   Web of Science ®Google Scholar
• Stehlík, M. 2006. Exact likelihood ratio scale and homogeneity testing of some loss processes. Stat. Probability Lett., 76, 19–26.
   Web of Science ®Google Scholar
• Stehlík, M. 2007. Exact testing of the scale with the missing time-to-failure information. Commun. Dependability Qual. Manage. Eng. (CDQM), 10(2), 124–129.
   Google Scholar
• Stehlík, M. 2008. Homogeneity and scale testing of generalized gamma distribution. Reliability Eng. System Safety, 93, 1809–1813.
   Web of Science ®Google Scholar
• Stehlík, M. 2009. Scale testing in small samples with missing time-to-failure information. Int. J. Reliability Qual. Safety Eng. (IJRQSE), 16(6), 1–13.
   Google Scholar
• Stehlík, M., R. Potocký, H. Waldl, and Z. Fabián. 2010. On the favourable estimation of fitting heavy tailed data. Comput. Stat., 25, 485–503.
   Web of Science ®Google Scholar
• Stehlík, M., and H. Wagner. 2011. Exact likelihood ratio testing for homogeneity of exponential distribution. Commun. Stat. Simulation Comput., 40, 663–684.
   Web of Science ®Google Scholar
• Stehlík, M., P. Economou, J. Kise[lbreve]ák, and W.-D. Richter. 2014. Kullback–Leibler life time testing. App. Math. Comput., 240, 122–139.
   Web of Science ®Google Scholar
• Sukhatme, P. V. 1937. Tests of significance for samples of the χ2 population with two degrees of freedom. Ann. Eugenics, 8, 52–56.
   Google Scholar
• Thiagarajah, K. R. 1995. Homogeneity tests for scale parameters of 2-parameter exponential populations under time censoring. IEEE Trans. Reliability. 44(2), 297–301.
   Web of Science ®Google Scholar
• Thomas, D. R., and W. M. Wilson. 1972. Linear order statistic estimation for the two parameter Weibull and extreme value distributions from Type-II progressively censored samples. Technometrics, 14, 679–691.
   Web of Science ®Google Scholar
• Usher, J. S. 1996. Weibull component reliability—Prediction in the presence of masked data. IEEE Trans. Reliability, 45, 229–232.
   Web of Science ®Google Scholar
• Viveros, R., and N. Balakrishnan. 1994. Interval estimation of parameters of life from progressively censored data. Technometrics, 36(1), 84–91.
   Web of Science ®Google Scholar
• Wilks, S. S. 1962. Mathematical statistics. New York, NY: John Wiley & Sons.
   Google Scholar
• Wu, S. J., D. H. Chen, and S. T. Chen. 2006. Bayesian inference for Rayleigh distribution under progressive censored sample. App. Stochastic Models Business Ind., 22, 269–279.
   Web of Science ®Google Scholar