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Original Articles

Adjusted profile likelihoods for the weibull shape parameter

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Pages 531-548 | Received 23 Mar 2005, Published online: 01 Aug 2007

References

  • Mann , N. R. , Schafer , R. E. and Singpurwalla , N. D. 1974 . Methods for Statistical Analysis and Reliability and Life Data , New York : Wiley .
  • Gross , A. J. and Clark , V. A. 1975 . Survival Distribution: Reliability Applications in the Biomedical Sciences , New York : Wiley .
  • Lawless , J. F. 1982 . Statistical Models and Methods for Lifetime Data , New York : Wiley .
  • Klein , J. P. and Moeschberger , M. 1997 . Survival Analysis , New York : Springer–Verlag .
  • Ageel , M. I. 2002 . A novel means of estimating quantiles for 2-parameter Weibull distribution under the right random censoring model . Journal of Computational and Applied Mathematics , 149 : 373 – 380 .
  • Bar-Lev , S. K. 2004 . Likelihood-based inference for the shape parameter of a two parameter Weibull distribution . Lifetime Data Analysis , 10 : 293 – 308 .
  • Lu , H. L. , Chen , C. H. and Wu , J. W. 2004 . A note on weighted least-squares estimation of the shape parameter of the Weibull distribution . Quality and Reliability Engineering International , 20 : 579 – 586 .
  • Maswadah , M. 2003 . Conditional confidence interval estimation for the inverse Weibull distribution based on censored generalized order statistics . Journal of Statistical Computation and Simulation , 73 : 887 – 898 .
  • Yang , Z. and Xie , M. 2003 . Efficient estimation of the Weibull shape parameter based on a modified profile likelihood . Journal of Statistical Computation and Simulation , 73 : 115 – 123 .
  • Cox , D. R. and Reid , N. 1987 . Parameter orthogonality and approximate conditional inference . Journal of the Royal Statistical Society B , 49 : 1 – 39 .
  • Barndorff-Nielsen , O. E. 1980 . Conditionality resolutions . Biometrika , 67 : 293 – 310 .
  • Barndorff-Nielsen , O. E. 1983 . On a formula for the distribution of the maximum likelihood estimator . Biometrika , 70 : 343 – 365 .
  • Severini , T. A. 2000 . Likelihood Methods in Statistics , Oxford : Oxford University Press .
  • Severini , T. A. 1998 . An approximation to the modified profile likelihood function . Biometrika , 85 : 403 – 411 .
  • Severini , T. A. 1999 . An empirical adjustment to the likelihood ratio statistic . Biometrika , 86 : 235 – 247 .
  • Fraser , D. A.S. and Reid , N. 1995 . Ancillaries and third-order significance . Utilitas Mathematica , 47 : 33 – 53 .
  • Fraser , D. A.S. , Reid , N. and Wu , J. 1999 . A simple formula for tail probabilities for frequentist and Bayesian inference . Biometrika , 86 : 655 – 661 .
  • Doornik , J. A. 2001 . Ox: an Object-oriented Matrix Language , 4th , London : Timberlake Consultants Press . http://www.doornik.com
  • Proschan , F. 1963 . Theoretical explanation of observed decreasing failure rate . Technometrics , 5 : 375 – 383 .
  • Mann , N. R. and Fertig , K. W. 1973 . Tables for obtaining confidence bounds and tolerance bounds based on best linear invariant estimates of parameters of the extreme value distribution . Technometrics , 15 : 87 – 101 .
  • Cox , D. R. and Reid , N. 1989 . On the stability of maximum-likelihood estimators of orthogonal parameters . Canadian Journal of Statistics , 17 : 229 – 233 .
  • Lai , C. D. , Zhang , L. and Xie , M. 2004 . Mean residual life and other properties of Weibull related bathtub shape failure rate distributions . International Journal of Reliability, Quality and Safety Engineering , 11 : 113 – 132 .
  • Murthy , D. N.P. , Xie , M. and Jiang , R. 2003 . Weibull Models , New York : Wiley .
  • Xie , M. , Lai , C. D. and Murthy , D. N.P. 2003 . “ Weibull-related distributions with bathtub shaped failure rate functions ” . In Mathematical and Statistical Methods in Reliability , Edited by: Doksum , K. and Lindqvist , B. Vol. 7 , 283 – 297 . Singapore : World Scientific Publishing Co .
  • Xie , M. , Goh , T. N. and Tang , Y. 2002 . A modified Weibull extension with bathtub-shaped failure rate function . Reliability Engineering and Systems Safety , 76 : 279 – 285 .
  • Thoman , D. R. , Bain , L. J. and Antle , C. E. 1969 . Inferences on the parameters of the Weibull distribution . Technometrics , 11 : 445 – 460 .

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