165
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Predictive Inference from the Half-Normal Model Given a Type II Censored Sample

Pages 42-55 | Received 18 Nov 2010, Accepted 13 Apr 2011, Published online: 03 Dec 2012

References

  • Aitchison , J. , Dunsmore , I. R. ( 1975 ). Statistical Prediction Analysis . New York : Cambridge University Press .
  • Aitchison , J. , Sculthorpe , D. ( 1965 ). Some problems of statistical prediction . Biometrika 52 : 469 – 483 .
  • Ali Mousa , M. A. M. , Al-Sagheer , S. A. ( 2006 ). Statistical inference for the Rayleigh model based on progressively type-II censored data . Statistics 40 ( 2 ): 149 – 157 .
  • Bain , L. J. , Engelhardt , M. ( 1991 ). Statistical Analysis of Reliability and Life Testing Models: Theory and Methods . New York : Marcel Dekker Inc .
  • Berger , J. O. ( 1985 ). Statistical Decision Theory and Bayesian Analysis . New York : Springer-Verlag .
  • Bernardo , J. M. , Smith , A. F. M. ( 2000 ). Bayesian Theory . New York : Wiley .
  • Bogdanoff , D. A. , Pierce , D. A. ( 1973 ). Bayes-Fiducial inference for the Weibull distribution . J. Amer. Statist. Assoc. 68 ( 343 ): 659 – 664 .
  • Chew , V. ( 1968 ). Simultaneous prediction intervals. Technometrics pp. 323–330 .
  • Cooray , K. , Ananda , M. M. A. ( 2008 ). A generalization of the half-normal distribution with applications to lifetime data . Commun. Statist. Theor. Meth. 37 ( 9 ): 1323 – 1337 .
  • Evans , I. G. , Nigm , A. M. ( 1980a ). Bayesian prediction for two-parameter Weibull Lifetime Models . Commun. Statist. Theor. Meth. A9 ( 6 ): 649 – 658 .
  • Evans , I. G. , Nigm , A. H. M. ( 1980b ). Bayesian prediction for the left truncated exponential distribution . Technometrics 22 ( 2 ): 201 – 204 .
  • Fernandez , A. J. ( 2000a ). On maximum lilelihood prediction based on Type II doubly censored exponential data . Metrika 50 : 211 – 220 .
  • Fernandez , A. J. ( 2000b ). Bayesian inference from Type II doubly censored Rayleigh data . Statist. Probab. Lett. 48 : 393 – 399 .
  • Geisser , S. ( 1971 ). The inferential use of predictive distributions . In: Godambe , V. P. , Sprott , D. A. Eds. , Foundation of Statistical Inference . Toronto : Holt , pp. 456 – 69 .
  • Geisser , S. ( 1993 ). Predictive Inference: An Introduction . New York : Chapman and Hall .
  • Gelman , A. , Carlin , J. B. , Stern , H. S. , Rubin , D. B. ( 2004 ). Bayesian Data Analysis . New York : Chapman and Hall/CRC .
  • Hossain , A. , Howlader , H. A. ( 1995 ). On Bayesian estimation and prediction from Rayleigh based on Type II censored data . Commun. Statist. Theor. Meth. 24 ( 9 ): 2249 – 59 .
  • Hui , G. E. ( 1980 ). Prediction distribution for some life testing models. Ph.D. Thesis, The University of Western Ontario, Canada .
  • Khan , H. M. R. ( 2003 ). Predictive inference for certain life testing models. Ph.D. Thesis, The University of Western Ontario, Canada .
  • Khan , H. M. R. , Haq , M. S. , Provost , S. B. ( 2003 ). Predictive distribution for responses from the two-parameter exponential life testing model . J. Appl. Statist. Sci. 12 ( 2 ): 137 – 156 .
  • Khan , H. M. R. , Haq , M. S. , Provost , S. B. ( 2004 ). Predictive distributions for responses from the Weibull life testing model . J. Statist. Theor. Applic 3 ( 1 ): 53 – 73 .
  • Khan , H. M. R. , Haq , M. S. , Provost , S. B. ( 2006 ). Predictive inference for future responses given a doubly censored sample from a two parameter exponential distribution . J. Statist. Plann. Infer. 136 ( 9 ): 3156 – 3172 .
  • Khan , H. M. R. , Provost , S. B. , Hegele , R. A. ( 2007 ). Bayesian applications in cytogenetic studies . J. Appl. Probab. Statist. 2 ( 2 ): 157 – 172 .
  • Khan , H. M. R. , Faysel , M. , Provost , S. B. ( 2008 ). A Bayesian approach to measure mRNA quality levels for microarray experiments . Int. J. Med. Eng. Informatics 1 ( 1 ): 125 – 133 .
  • Khan , H. M. R. , Provost , S. B. ( 2008 ). On predictive inference for future responses from the compound exponential model . J. Appl. Probab. Statist. 3 ( 2 ): 263 – 274 .
  • Khan , H. M. R. , Provost , S. B. , Singh , A. ( 2010 ). Predictive inference from a two-parameter Rayleigh life model given a doubly censored sample . J. Commun. Statist. Theor. Meth. 39 ( 7 ): 1237 – 1246 .
  • Khan , S. (2004). Predictive distribution of regression vector and residual sum of squares for normal multiple regression model. Commun. Statist. Theor. Meth. 33(10):2423–2443.
  • Khan , S. ( 2006 ). Prediction distribution of future regression and residual sum of squares matrices for multivariate simple regression model with correlated normal responses . J. Appl. Probab. Statist. 1 : 15 – 30 .
  • Khan , S. , Kabir , E. ( 2005 ). Distribution of future location vector and residual sum of squares for multivariate location-scale model with spherically contoured errors . J. Statist. Theor. Appl. 5 ( 2 ): 91 – 104 .
  • Kim , D. H. , Lee , W. D. , Kang , S. G. ( 2000 ). Bayesian model selection for life time data under Type II censoring . Commun. Statist. Theor. Meth. 29 ( 12 ): 2865 – 2878 .
  • Lawless , J. F ( 1971 ). A prediction problem concerning sample from the exponential distribution with application to life testing . Technometrics 13 : 725 – 730 .
  • Lawless , J. F ( 1977 ). Prediction intervals for two parameter exponential distribution . Technometrics 19 : 469 – 472 .
  • Lindley , D. V. ( 1971 ). Bayesian Statistics: A Review . Bristol , England : J. W. Arrowsmith Ltd .
  • Martz , H. F. , Waller , R. ( 1982 ). Bayesian Reliability Analysis . New York : Wiley .
  • Nigm , A. M. ( 1989 ). An informative Bayesian prediction for the Weibull lifetime distribution . Commun. Statist. 18 ( 3 ): 897 – 911 .
  • Pewsey , A. ( 2002 ). Large-sample inference for the general half-normal distribution . Commun. Statist. Theor. Meth. 31 : 1045 – 1054 .
  • Pewsey , A. ( 2004 ). Improved based inference for the general half-normal distribution . Commun. Statist. Theor. Meth. 33 : 197 – 204 .
  • Raiffa , H. , Schlaifer , R. ( 1961 ). Applied statistical decision Theory. Division of Research, Harvard Business School Boston .
  • Raqab , M. Z. ( 1995 ). On the maximum likelihood prediction of the exponential distribution based on double Type II censored samples . Pak. J. Statist. 11 ( 1 ): 1 – 10 .
  • Savage , L. J. ( 1954 ). The Foundations of Statistics . New York : John Wiley .
  • Sinha , S. K. ( 1986 ). Reliability and Life Testing . New York : John Wiley & Sons Inc .
  • Thabane , L. ( 1998 ). Contribution of Bayesian Statistical Inference. Ph.D. Thesis, The University of Western Ontario, Canada .
  • Thabane , L. , Haq , M. S. ( 2000 ). Bayesian prediction from a compound statistical model: An actual application . Pak. J. Statist. 16 ( 2 ): 110 – 125 .
  • Wiper , M. P. , Girón , F. J. , Pewsey , A. ( 2008 ). Objective Bayesian inference for the half-normal and half-t distributions . Commun. Statist. Theor. Meth. 37 ( 20 ): 3165 – 3185 .
  • Wolfram Research . ( 2008 ). The Mathematica Archive: Mathematica 7.0. Wolfram Research Inc., Illinois

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.