Reliability Functions of Bivariate Distributions in Modeling Marked Point Processes

REFERENCES

• Arnold , B.C. Bivariate distributions with Pareto conditionals . Stat. Probab. Lett. 1987 , 5 , 263 – 266 .
   Web of Science ®Google Scholar
• Arnold , B.C. ; Castillo , E. ; Sarabia , J.M. Conditionally specified distributions . Lecture Notes in Statistics ; Berlin : Springer , 1992 ; Vol. 73 .
   Google Scholar
• Arnold , B.C. ; Castillo , E. ; Sarabia , J.M. Multivariate distributions with generalized Pareto conditionals . Stat. Probab. Lett. 1993 , 17 , 361 – 368 .
   Google Scholar
• Arnold , B.C. ; Castillo , E. ; Sarabia , J.M. General conditional specification models . Comm. Stat. Theor. Meth. 1995 , 24 ( 1 ), 1 – 11 .
   Web of Science ®Google Scholar
• Barlow , R.E. ; Marshall , A.W. ; Proschan , F. Properties of probability distributions with monotone hazard rate . Ann. Math. Stat. 1963 , 34 , 375 – 389 .
   Google Scholar
• Barlow , R.E. ; Proschan , F. Statistical Theory and Life Testing ; Holt , Rinehart and Winston : New York , 1975 .
   Google Scholar
• Castillo , E. ; Galambos , J. Bivariate distributions with normal conditionals . In Proceedings of the International Symposium on Simulation, Modeling and Development ; Anaheim , CA , 1987 ; 59 – 62 .
   Google Scholar
• Castillo , E. ; Galambos , J. Conditional distributions and the bivariate normal distribution . Metrika 1989 , 36 , 209 – 214 .
   Google Scholar
• Clayton , D.G. A model for association in bivariate life tables and its applications in epidemiological studies of familial tendency in chronic disease incidence . Biometrika 1978 , 65 , 141 – 151 .
   Web of Science ®Google Scholar
• Elandt-Johnson , R.C. ; Johnson , N.L. Survival Models and Data Analysis ; John Wiley and Sons : New York , 1980 .
   Google Scholar
• Gaynor , J.J. ; Feuer , E.J. ; Tan , C.C. ; Wu , D.H. ; Little , C.R. ; Straus , D.J. ; Clarkson , B.D. ; Brennan , M.F. On the use of cause-specific failure and conditional failure probabilities: example from clinical oncology data . J. Am. Stat. Assoc. 1993 , 88 ( 422 ), 400 – 409 .
   Web of Science ®Google Scholar
• Glaser , R.E. Bath tub and related failure rate characterizations. J. Am. Stat. Assoc. 1980, 75, 667–672.
   Web of Science ®Google Scholar
• Gupta , R.C. Some counter examples in competing risk analysis . Comm. Stat. A 1979 , 8 ( 15 ), 1535 – 1540 .
   Web of Science ®Google Scholar
• Gupta , R.C. Non-monotonic failure rates and mean residual life functions . In System and Bayesian Reliability ; Hayakawa , Y. , Irony , T. , Xie , M. , Eds.; World Scientific : River Ridge , NJ , 2001 ; 147 – 162 .
   Google Scholar
• Gupta , R.C. ; Akman , O. Mean residual life function for certain types of non-monotonic ageing . Stoc. Model. 1995 11 ( 1 ), 219 – 225 .
   Google Scholar
• Gupta , R.C. ; Gupta , R.D. ; Gupta , P.L. Monotonicity of the (reversed) hazard rate of the (maximum) minimum in bivariate distributions . Metrika 2006 , 63 , 223 – 241 .
   Web of Science ®Google Scholar
• Gupta , R.C. ; Warren , W. Determination of change point of non-monotonic failure rates . Comm. Stat. Theor. Meth. 2001 , 30 ( 8&9 ), 1903 – 1920 .
   Google Scholar
• Hanley , J.A. ; Parnes , M.N. Nonparametric estimation of mutivariate distribution in the presence of censoring . Biometrika 1983 , 39 , 129 – 139 .
   Google Scholar
• Hassan , M.Y. ; Lii , K.-S. Modeling marked point processes via bivariate mixture transition distribution models . J. Am. Stat. Assoc. 2006 , 101 , 1241 – 1252 .
   Web of Science ®Google Scholar
• Holland , P.W. ; Wang , Y.J. Dependence function for continuous bivariate densities . Comm. Stat. Theor. Method. 1987 , 16 , 863 – 876 .
   Web of Science ®Google Scholar
• Joe , H. Multivariate Models and Dependence Concepts ; Chapman and Hall : New York , 1997 .
   Google Scholar
• Johnson , N.L. ; Kotz , S. A vector valued multivariate hazard rate . J. Multivariate Anal. 1975 , 5 , 53 – 66 .
   Google Scholar
• Manatunga , A.K. ; Oakes , D. A measure of association for bivariate frailty distributions . J. Multivariate Anal. 1996 , 56 , 60 – 74 .
   Web of Science ®Google Scholar
• Marshall , A.W. ; Olkin , I. Life Distributions ; Springer Verlag : New York , 2007 .
   Google Scholar
• Oakes , D. Bivariate survival models induced by frailties . J. Am. Stat. Assoc. 1989 , 84 , 487 – 493 .
   Web of Science ®Google Scholar
• Sarabia , J.M. The centered normal distribution . Comm. Stat. Theor. Method. 1995 , 24 ( 11 ), 2889 – 2900 .
   Web of Science ®Google Scholar
• Shaked , M. A family of concepts of dependence for bivariate distributions . J. Am. Stat. Assoc. 1977 , 72 , 642 – 650 .
   Web of Science ®Google Scholar