Higher order inference for stress–strength reliability with independent Burr-type X distributions

References

• Wolfe DA, Hogg RV. On constructing statistics and reporting data. Am Statist. 1971;25:27–30. doi: 10.2307/2682922
   Web of Science ®Google Scholar
• Hanley JA. Receiver operating characteristic(ROC) methodology: the state of the art. Crit Rev Diagnostic Imag. 1989;29:307–335.
   PubMedGoogle Scholar
• Burr IW. Cumulative frequency functions. Ann Math Stat. 1942;13:215–222. doi: 10.1214/aoms/1177731607
   Google Scholar
• Raqab MZ, Kundu D. Burr type X distribution: revisited. J Probab Statist Sci. 2006;2:179–193.
   Google Scholar
• Mudholkar GS, Srivastava DK. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab. 1993;42:299–302. doi: 10.1109/24.229504
   Web of Science ®Google Scholar
• Sartawi HA, Abu-Salih MS. Bayesian prediction bounds for the Burr type X model. Commun Stat – Theory Methods. 1991;20:2307–2330. doi: 10.1080/03610929108830633
   Web of Science ®Google Scholar
• Jaheen ZF. Bayesian approach to prediction with outliers from the Burr type X model. Microelectronics Reliab. 1995;35:45–47. doi: 10.1016/0026-2714(94)00056-T
   Web of Science ®Google Scholar
• Jaheen ZF. Empirical Bayes estimation for the reliability and failure rate function of Burr type X failure model. J Appl Statist Sci. 1996;3:281–288.
   Google Scholar
• Ahmad KE, Fakhry ME, Jaheen ZF. Empirical Bayes estimation of P(Y<X) and characterizations of the Burr-type X model. J Statist Plann Inference. 1997;64:297–308. doi: 10.1016/S0378-3758(97)00038-4
   Web of Science ®Google Scholar
• Surles JG, Padgett WJ. Some properties of a scaled Burr type X distribution. J Statist Plann Inference. 2005;128:271–280. doi: 10.1016/j.jspi.2003.10.003
   Web of Science ®Google Scholar
• Raqab MZ, Kundu D. Comparison of different estimators of P(Y<X) for a scaled Burr type X distribution. Commun Stat – Simul Comput. 2005;34:465–482. doi: 10.1081/SAC-200055741
   Web of Science ®Google Scholar
• Surles JG, Padgett WJ. Inference for P(Y<X) in the Burr type X model. J Appl Statist Sci. 1998;7:225–238.
   Google Scholar
• Surles JG, Padgett WJ. Inference for reliability and stress–strength for a scaled Burr type X distribution. Lifetime Data Anal. 2001;7:187–200. doi: 10.1023/A:1011352923990
   PubMed Web of Science ®Google Scholar
• Ventura L, Racugno W. Recent advances on Bayesian inference for P(X<Y). Bayesian Anal. 2011;6:411–428. doi: 10.1214/ba/1339616470
   Web of Science ®Google Scholar
• Cortese G, Ventura L. Accurate higher-order likelihood inference on P(Y<X). Comput Stat. 2013;28:1035–1059. doi: 10.1007/s00180-012-0343-z
   Web of Science ®Google Scholar
• Cox DR, Hinkley DV. Thoeretical statistics. London: Chapman & Hall; 1974.
   Google Scholar
• Doganaksoy N, Schmee J. Comparisons of approximate confidence intervals for distributions used in life-data analysis. Technometrics. 1993;35:175–184. doi: 10.1080/00401706.1993.10485039
   Web of Science ®Google Scholar
• Reid N. Likelihood and higher-order approximations to tail areas: a review and annotated bibliography. Can J Stat. 1996;24:141–166. doi: 10.2307/3315622
   Web of Science ®Google Scholar
• Severeni T. Likelihood methods in statistics. New York: Oxford University Press; 2000.
   Google Scholar
• Barndorff-Nielsen OE. Inference on full or partial parameters based on the standardized signed log likelihood ratio. Biometrika. 1986;73:307–322.
   Web of Science ®Google Scholar
• Barndorff-Nielsen OE. Modified signed log likelihood ratio. Biometrika 1991;78:557–563. doi: 10.1093/biomet/78.3.557
   Web of Science ®Google Scholar
• Fraser DAS, Reid N. Ancillaries and third order significance. Utilitas Mathematica. 1995;47:33–35.
   Google Scholar
• Fraser DAS, Reid N, Wu J. A simple general formula for tail probabilities for frequentist and Bayesian inference. Biometrika. 1999;86:249–264. doi: 10.1093/biomet/86.2.249
   Web of Science ®Google Scholar
• Mudholkar GS, Srivastava DK, Freimer M. The Exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics. 1995;37:436–445. doi: 10.1080/00401706.1995.10484376
   Web of Science ®Google Scholar
• Byrd RH, Lu P, Nocedal J, Zhu C. A limited memory algorithm for bound constrained optimization. SIAM J. Sci Comput. 1995;16:1190–1208. doi: 10.1137/0916069
   Web of Science ®Google Scholar
• Badar MG, Priest AM. Statistical aspects of fibre and bundle strength in hybrid composites. In: Hayashi T, Kawata K, Umekawa S, editors. Progress in science and engineering composites. ICCM-IV. Tokyo: Japan Society of Composite Materials; 1982; p. 1129–1136.
   Google Scholar