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RELIABILITY AND SURVIVAL ANALYSIS

A Mixture Model of Proportional Reversed Hazard Rate

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Pages 2953-2963 | Received 28 Sep 2007, Accepted 12 Mar 2008, Published online: 31 Jul 2008

References

  • Aalen , O. O. ( 1988 ). Heterogeneity in survival analysis . Statist. Med. 7 : 1121 – 1137 .
  • Aalen , O. O. ( 1992 ). Modeling heterogeneity in survival analysis by the compound Poisson distribution . Ann. Appl. Probab. 2 : 951 – 972 .
  • Barlow , R. E. , Proschan , F. ( 1981 ). Statistical Theory of Reliability and Life Testing . Silver Spring , MD : To Begin with .
  • Beard , R. E. ( 1959 ). Note on some mathematical mortality models . In : Woolstenholme , G. E. W. , O'onnor , M. , eds. The Lifespan of Animals . Boston : Little .
  • Block , H. , Savits , T. , Singh , H. ( 1998 ). The reversed hazard rate function . Probab. Eng. Information. Sci. 12 : 69 – 90 .
  • Chandra , N. N. , Roy , D. ( 2001 ). Some results on reversed hazard rate function . Probab. Eng. Information. Sci. 15 : 95 – 102 .
  • Crescenzo , A. D. ( 2000 ). Some results on the proportional reversed hazard model . Statist. Probab. Lett. 50 : 313 – 321 .
  • Eeckhoudt , L. , Gollier , C. ( 1995 ). Demand for risky assets and the monotone probability ratio order . J. Risk Uncertainty 11 : 113 – 122 .
  • Finkelstein , M. S. ( 2004 ). Minimal repairs in heterogeneous populations . J. Appl. Probab. 41 : 281 – 286 .
  • Finkelstein , M. S. ( 2005 ). Why the mixture failure rate bends down with time . South African Statist. J. 39 : 23 – 33 .
  • Finkelstein , M. S. , Esaulova , V. ( 2006 ). On mixture failure rate ordering . Commun. Statist. Theor. Meth. 35 : 1943 – 1955 .
  • Gupta , R. D. , Nanda , A. K. ( 2001 ). Some results on reversed hazard rate ordering . Commun. Statist. Theor. Meth. 30 ( 11 ): 2447 – 2458 .
  • Gupta , R. C. , Wu , H. ( 2001 ). Analyzing survival data by proportional reversed hazard model . Int. J. Reliab. Applic. 2 ( 1 ): 1 – 26 .
  • Gupta , R. C. , Kirmani , S. N. U. A. ( 2006 ). Stochastic comparisons in frailty models . J. Statist. Plann. Infer. 136 ( 10 ): 3647 – 3658 .
  • Gupta , R. C. , Gupta , R. D. ( 2007 ). Proportional reversed hazard rate model and its applications . J. Statist. Plann. Infer. 137 ( 11 ): 3525 – 3536 .
  • Gupta , R. C. , Gupta , P. L. , Gupta , R. D. ( 1998 ). Modeling failure time data by Lehman alternatives . Commun. Statist. Theor. Meth. 27 ( 4 ): 887 – 904 .
  • Hougaard , P. ( 1984 ). Life table methods for heterogeneous population: distribution describing the heterogeneity . Biometrika 71 : 75 – 83 .
  • Hougaard , P. ( 1991 ). Modelling heterogeneity in survival analysis . J. Appl. Probab. 28 : 695 – 701 .
  • Joe , H. ( 1997 ). Multivariate Models and Dependence Concepts . London : Chapman and Hall .
  • Kalbfliesch , J. D. , Lawless , J. F. ( 1989 ). Inference based on retrospective ascertainment: An analysis of the data on transfusion-related AIDS . J. Amer. Statist. Assoc. 84 : 360 – 372 .
  • Kijima , M. ( 1998 ). Hazard rate and reversed hazard rate monotonicities in continuous time Markov chains . J. Appl. Probab. 35 : 545 – 556 .
  • Kijima , M. , Ohnishi , M. ( 1999 ). Stochastic orders and their application in financial optimization . Mathemat. Meth. Operations Res. 50 : 351 – 372 .
  • Lehman , E. L. ( 1953 ). The power of rank tests . Ann. Mathemat. Statist. 24 : 28 – 43 .
  • Li , X. , Zuo , M. J. ( 2004 ). Stochastic comparison of residual life and inactivity time at a random time . Stochastic Mod. 20 ( 2 ): 229 – 235 .
  • Müller , A. , Stoyan , D. ( 2002 ). Comparison Methods for Stochastic Models and Risks . New York : John Wiley & Sons .
  • Navarro , J. , Belzunce , F. , Ruiz , J. M. ( 1997 ). New stochastic orders based on double truncation . Probab. Eng. Information. Sci. 11 : 395 – 402 .
  • Nelsen , R. B. ( 1999 ). An Introduction to Copulas . Lecture Notes in Statistics . New York : Springer .
  • Sengupta , D. , Nanda , A. K. (1999). Logconcave and concave distributions in reliability. Nav. Res. Logistics Quart. 46(4):419–433.
  • Shaked , M. , Shanthikumar , J. G. ( 1994 ). Stochastic Orders and Their Applications . San Diego , CA : Academic Press .
  • Shaked , M. , Shanthikumar , J. G. ( 2007 ). Stochastic Orders . New York : Springer-Verlag .
  • Tsodikov , A. D. , Aselain , B. , Yakovlev , A. Y. ( 1997 ). A distribution of tumor size at detection: an application to breast cancer data . Biometrics 53 : 1495 – 1502 .
  • Vaupel , J. W. , Manton , K. G. , Stallard , E. ( 1979 ). The impact of heterogeneity in individual frailty on the dynamics of mortality . Demography 16 : 439 – 454 .
  • Xu , M. , Li , X. ( 2008 ). Negative dependence in frailty models . J. Statist. Plann. Infer. 138 ( 5 ): 1433 – 1441 .

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