AGEING AND RISK ASPECTS IN PREDICTIVE INFERENCE BASED ON PROPORTIONAL HAZARD MODELS
Keywords:
Archimedean copulas, Conditional IFR and DFR, Hazard rate ordering, Likelihood ratio, Majorization, More PQD, Stochastic ordering of posterior distributions, Two- actions decision problems.Abstract
Proportional Hazard Models arise from a straightforward generalization of the simple case of conditionally i.i.d., exponentially distributed random variables and, in a sense, can be considered as the idealized models in the statistical analysis of failure and survival data for lifetimes. For these reasons, they have been extensively studied in the literature. Despite of the richness of related contributions, there are still special aspects of these models that are worthwhile focusing. In this discussion paper we aim to present some contributions, in the frame of a Bayesian approach and by using some very basic notions of stochastic ordering.
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References
Averous J. and Dortet-Bernadet J. L. (2004). Dependence for Archimedean
copulas and aging properties of their generating functions. Sankhya 66, p. 607-
-620.
Barlow R. E. and Proschan F. (1975). Statistical Theory of Reliability and
Life Testing. Holt, Rinehart and Winston, New York.
Barlow R. E. and Spizzichino F.(1993). Schur-concave survival functions and
survival analysis. J. Comp. and Appl. Math. 46, p. 437--447.
Bassan B. and Spizzichino F. (1999). Stochastic comparison for residual
lifetimes and Bayesian notions of multivariate ageing. Adv. In Appl. Probab.
, p. 1078--1094.
Bassan B. and Spizzichino F. (2003). On some properties of dependence and
aging for residual life-times in the exchangeable case. Mathematical and
Statistical Methods in Reliability, World Scientific.
Caramellino L. and Spizzichino F. (1996). WBF property and stochastic
monotonicity of the Markov Process associated to Schur-constant survival
functions. J. Multiv. Anal, 56, p. 153--163.
Charpentier A. (2006). Dependence structure and limiting results: some
applications in finance and insurance. PhD thesis, Katholieke Universiteit
Leuven.
Durante F. and Jaworski P. (2010). Spatial contagion between financial
markets: a copula-based approach. Appl. Stoch. Models Bus. Ind. 26, p. 551--
Fahmy S., de B. Pereira C. A., Proschan F. and Shaked M. (1982). The
influence of the sample on the posterior distribution. Comm. Statist. - A.
Theory and Methods, 11, p. 1757--1768.
Joe, H. (1997). Multivariate models and dependence concepts, Monographs on
Statistics and Applied Probability, vol.73. Chapman & Hall, London.
Karlin S. and Rinott Y. (1980). Classes of orderings measures and related
correlation inequalities. I, Multivariate totally positive distributions. J. Mult.
An., 10, p. 467--498.
Khaledi B.E. and Kochar S. (2001). Dependence properties of multivariate
mixture distributions and their applications. Ann. Inst. Statist. Math., 53, p.
--630.
Lai C.D. and Xie M. (2006). Stochastic Ageing and Dependence for
Reliability. Springer-Verlag, New York.
Marshall A. and Olkin (1979). Inequalities: Theory of Majorization and its
Applications. Academic Press, New York.
Marshall A. and Olkin I. (1988). Families of Multivariate Distributions. J.
Amer. Statist. Soc. 83, p. 834--841
