Predictive Inference from a Two-Parameter Rayleigh Life Model Given a Doubly Censored Sample

References

• Aitchison , J. , Dunsmore , I. R. ( 1975 ). Statistical Prediction Analysis . New York : Cambridge University Press .
   Google Scholar
• Aitchison , J. , Sculthorpe , D. ( 1965 ). Some problems of statistical prediction . Biometrika 52 : 469 – 483 .
   PubMed Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Berger , J. O. ( 1985 ). Statistical Decision Theory and Bayesian Analysis . New York : Springer-Verlag .
   Google Scholar
• Bernardo , J. M. , Smith , A. F. M. ( 1994 ). Bayesian Theory . New York : Wiley .
   Google Scholar
• Chew , V. ( 1968 ). Simultaneous prediction intervals . Technometrics 323 – 330 .
   Web of Science ®Google Scholar
• Cochran W. G. ( 1977 ). Sampling Techniques . New York : John Wiley & Sons , pp. 109 – 113 .
   Google Scholar
• Evans , I. G. , Nigm , A. M. ( 1980a ). Bayesian prediction for two-parameter Weibull lifetime models . Commun. Statist. Theor. Meth. A9 ( 6 ): 649 – 658 .
   Web of Science ®Google Scholar
• Evans , I. G. , Nigm , A. H. M. ( 1980b ). Bayesian prediction for the left truncated exponential distribution . Technometrics 22 ( 2 ): 201 – 204 .
   Web of Science ®Google Scholar
• Fernandez , A. J. ( 2000a ). On maximum lilelihood prediction based on Type II doubly censored exponential data . Metrika 50 : 211 – 220 .
   Web of Science ®Google Scholar
• Fernandez , A. J. ( 2000b ). Bayesian inference from Type II doubly censored Rayleigh data . Statist. Probab. Lett. 48 : 393 – 399 .
   Web of Science ®Google Scholar
• 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 – 469 .
   Google Scholar
• Geiser , S. ( 1993 ). Predictive Inference: An Introduction . New York : Chapman and Hall .
   Google Scholar
• Gelman , A. , Carlin , J. B. , Stern , H. S. , Rubin , D. B. ( 2004 ). Bayesian Data Analysis . New York : Chapman and Hall/CRC .
   Google Scholar
• Gerald , V. B. , Fisher , L. D. , Heagerty , P. J. , Lumley , T. ( 2004 ). Biostatistics – A Methodology for the Health Sciences . New York : John Wiley & Sons Inc.
   Google Scholar
• 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 – 2259 .
   Web of Science ®Google Scholar
• Hui , G. E. ( 1980 ). Prediction Distribution for Some Life Testing Models . Unpublished Ph.D. thesis , The University of Western Ontario , London , Ontario , Canada .
   Google Scholar
• Ipsen , J. Jr. ( 1949 ). A practical method of estimating the mean and standard deviation of truncated normal distributions . Human Biol. 21 : 1 – 16 .
   PubMedGoogle Scholar
• Kambo , N. S. ( 1978 ). Maximum likelihood estimators of the location and scale parameters of the scale and location parameters of the exponential distribution from a censored sample . Commun. Statist. Theor. Meth. A 12 : 1129 – 1132 .
   Google Scholar
• Khan , H. M. R. ( 2003 ). Predictive Inference for Certain Life Testing Models . Ph.D. thesis . The University of Western Ontario , London , Ontario , Canada .
   Google Scholar
• 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 .
   Google Scholar
• Khan , H. M. R. , Haq , M. S. , Provost , S. B. ( 2004 ). Predictive distributions for responses from the Weibull life testing model . J. Statist. Theor. Appl. 3 ( 1 ): 53 – 73 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• Khan , H. M. R. , Provost , S. B. , Hegele , R. A. ( 2007 ). Bayesian applications in cytogenetic studies . J. Appl. Probab. Statist. 2 ( 2 ): 157 – 172 .
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• 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 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Lalitha , S. , Mishra , A. ( 1996 ). Maximum likelihood estimation for Rayleigh distribution . Commun. Statist. Theor Meth. 25 ( 2 ): 389 – 401 .
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• Sarhan , A. E. ( 1955 ). Estimation of the mean and standard deviation by order statistics. Part III . Ann. Math. Statist. 26 : 576 – 592 .
   Google Scholar
• Sinha , S. K. ( 1986 ). Reliability and Life Testing . New York : John Wiley & Sons Inc .
   Google Scholar
• Thabane , L. ( 1998 ). Contribution of Bayesian Statistical Inference . Ph.D. thesis , The University of Western Ontario , London , Ontario , Canada .
   Google Scholar
• Wolfram Research ( 2008 ). The Mathematica Archive: Mathematica 6.0 . Wolfram Research Inc. IL .
   Google Scholar