Some bivariate notions of IFR and DMRL and related properties

Journal of Applied Probability

Volumn 39, Issue 3, 2002, Pages 533-544

  Bassan, Bruno ^a   Kochar, Subhash ^b   Spizzichino, Fabio ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Ageing properties of mixtures; Log concavity; Mean residual life function; Multivariate extensions of IFR and DMRL; Residual lifetime; Schur concavity

Indexed keywords

EID: 18744367824     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1034082125     Document Type: Article

References (23)

1. Arjas, E. (1981). A stochastic process approach to multivariate reliability systems: notions based on conditional stochastic order. Math. Operat. Res. 6, 263-276.
2. Barlow, R.E. and Mendel, M.B. (1992). De Finetti-type representations for life distributions. J. Amer. Statist. Assoc. 87, 1116-1122.
3. Barlow, R.E. and Mendel, M.B. (1993). Similarity as a characteristic of ageing. In Reliability and Decision Making, eds R.E. Barlow, C.A. Clarotti and F. Spizzichino, Chapman and Hall, London, pp. 233-245.
4. Barlow, R. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.
5. Barlow, R.E. and Spizzichino, F. (1993). Schnr-concave survival functions and survival analysis. J. Comput. Appl. Math. 46, 437-447.
6. Bassan, B. and Spizzichino, F. (1999). Stochastic comparison for residual lifetimes and Bayesian notions of multivariate ageing. Adv. Appl. Prob. 31, 1078-1094.
7. Brindley, E.C. and Thompson, W.A. (1972). Dependence and aging aspects of multivariate survival. J. Amer. Statist. Assoc. 67, 822-830.
8. Deshpande, J.V., Kochar, S.C. and Singh, H. (1986). Aspects of positive ageing, J. Appl. Prob. 23, 748-58.
9. Finkelstein, M.S. and Esaulova, V. (2001). Modeling a failure rate for a mixture of distribution functions. Prob. Eng. Inf. Sci. 15, 383-400.
10. Guess, F. and Proschan, F. (1988). Mean residual life: theory and applications. In Handbook of Statistics, Vol. 7, Quality Control and Reliability, eds P.R. Krishnaiah and C.R. Rao, North-Holland, Amsterdam, pp. 215-224.
11. Karlin, S. (1968). Total Positivity. Stanford University Press.
12. Khaledi, B. and Kochar, S. (2000). Stochastic comparisons and dependence among concomitants of order statistics. J. Multivariate Anal. 73, 262-281.
13. Kochar, S., Mukerjee, H. AND Samaniego, F. (2000). Estimation of a monotone mean residual life. Ann. Statist. 28, 905-921.
14. Lynch, J.D. (1999). On conditions for mixtures of increasing failure rate distributions to have an increasing failure rate. Prob. Eng. Inf. Sci. 13, 33-36.
15. Marshall, A.W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.
16. Prékopa, A. (1973). On logarithmic concave measures and functions. Acta Sci. Math. (Szeged) 34, 335-343.
17. Savits, T.H. (1985). A multivariate IFR distribution. J. Appl. Prob. 22, 197-204.
18. Snaked, M. (1977). A family of concepts of dependence for bivariate distributions. J. Amer. Statist. Assoc. 72, 642-650.
19. Shaked, M. and Shanthikumar, J.G. (1988). Multivariate conditional hazard rates and the MIFRA and MIFR properties. J. Appl. Prob. 25, 150-168.
20. Shaked, M. and Shanthikumar, J.G. (1991). Dynamic multivariate aging notions in reliability theory. Stoch. Process. Appl. 38, 85-97.
21. Shaked, M. and Shanthikumar, J.G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego, CA.
22. Shaked, M. and Spizzichino, F. (2001). Mixtures and monotonicity of failure rate functions. In Handbook of Statistics, Vol. 20, Advances in Reliability, eds N. Balakrishnan and C.R. Rao, North-Holland, Amsterdam, pp. 185-198.
23. Spizzichino, F. (2001). Subjective Probability Models for Lifetimes. Chapman and Hall/CRC, Boca Raton, FL.