Properties of Some Stochastic Orders: A Unified Study

Naval Research Logistics

Volumn 51, Issue 2, 2004, Pages 193-216

  Hu, Taizhong ^a   Nanda, Asok K ^b   Xie, Huiliang ^a   Zhu, Zegang ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

DMRL; Hazard rate order; IFR; ILR; ILRs; Likelihood ratio order; Likelihood ratio order of degree s; Mean residual life order; Up shifted likelihood ratio order of degree s

Indexed keywords

FUNCTIONS; INTEGRAL EQUATIONS; ITERATIVE METHODS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; SET THEORY;

MEAN RESIDUAL LIFE ORDERS; STOCHASTIC ORDERS;

STOCHASTIC CONTROL SYSTEMS;

EID: 1642291367     PISSN: 0894069X     EISSN: None     Source Type: Journal    
DOI: 10.1002/nav.10111     Document Type: Article

References (32)

1. A.-H.N. Ahmed, Preservation properties for the mean residual life ordering, Statist Papers 29 (1988), 143-150.
2. A.N. Ahmed, A.A. Soliman, and S.E. Khider, On some partial ordering of interest in reliability, Microelectron Reliab 36 (1996), 1337-1346.
3. B. Bassan, M. Denuit, and M. Scarsini, Variability orders and mean differences, Statist Probab Lett 45 (1999), 121-130.
4. M. Brown and J.G. Shanthikumar, Comparing the variability of random variables and point processes, Probab Engrg Inform Sci 12 (1998), 425-444.
5. P. Capéraà, Tail ordering and asymptotic efficiency of rank tests, Ann Statist 16 (1988), 470-478.
6. M. Denuit, C. Lefèvre, and M. Shaked, The s-convex orders among real random variables, with applications, Math Inequal Appl 1 (1998), 585-613.
7. S. Dharmadhikari and K. Joag-dev, Unimodality, convexity and applications, Academic, New York, 1988.
8. E. Fagiuoli F. Pellerey, New partial orderings and applications, Naval Res Logist 40 (1993), 829-842.
9. O. Hesselager, Closure properties of some partial orderings under mixing, Insurance Math Econom 22 (1998), 163-170.
10. T. Hu, A. Kundu, and A.K. Nanda, "On generalized orderings and aging properties with their implications," System and Bayesian reliability, Y. Hayakawa, T. Irony, and M. Xie (Editors), World Scientific, Singapore, 2001, pp. 199-228.
11. T. Hu and Z. Zhu, An analytic proof of the preservation of the up shifted likelihood ratio order under convolutions, Stochastic Process Appl 95(1) (2001), 55-61.
12. K. Joag-dev, S. Kochar, and F. Proschan, A general composition theorem and its applications to certain partial orderings of distributions, Statist Probab Lett 22 (1995), 111-119.
13. R. Kaas, A.E. Van Heerwaarden, and M.J. Goovaerts, Ordering of actuarial risks, Institute for Actuarial Science and Econometrics, University of Amsterdam, Amsterdam, 1994.
14. S. Karlin, Total positivity, Stanford University Press, Stanford, CA, 1968, Vol. 1.
15. M.-L.T. Lee, Dependence by total positivity, Ann Probab 13 (1985), 572-582.
16. R.E. Lillo, A.K. Nanda, and M. Shaked, "Some shifted stochastic orders," Recent advances in reliability theory: Methodology, practice, and inference, N. Limnios and M. Nikulin (Editors), Birkhäuser, Boston, 2000, pp. 85-103.
17. C. Ma, Uniform stochastic ordering on a system of components with dependent lifetimes induced by a common environment, Sankhya√ Ser A 61 (1999), 218-228.
18. S.P. Mukherjee and A. Chatterjee, Stochastic dominance of higher orders and its implications, Commun Stat Theory Methods 21 (1992), 1977-1986.
19. A. Müller and D. Stoyan, Comparison methods for stochastic models and risks, Wiley, West Sussex, 2002.
20. A.K. Nanda, On improvement and deterioration of a repairable system, IAPQR Trans Reliab 22 (1997), 107-113.
21. A.K. Nanda, Generalized ageing classes in terms of Laplace transforms, Sankhya√ Ser A 62 (2000), 258-266.
22. A.K. Nanda, K. Jain, and H. Singh, Properties of moments for s-order equilibrium distributions, J Appl Probab 33 (1996), 1108-1111.
23. A.K. Nanda, K. Jain, and H. Singh, On closure of some partial orderings under mixtures, J Appl Probab 33 (1996), 698-706.
24. A.K. Nanda and M. Shaked, The hazard rate and the reversed hazard rate orders, with applications to order statistics, Ann Inst Stat Math 53 (2001), 863-864.
25. H.H. Panjer and G.E. Willmot, Insurance risk models, Society of Actuaries, Schaumburg, IL, 1992.
26. S.M. Ross, Stochastic processes, 2nd edition, Wiley, New York, 1996.
27. M. Shaked, A family of concepts of positive dependence for bivariate distributions, J Amer Statist Assoc 72 (1977), 642-650.
28. M. Shaked and J.G. Shanthikumar, Stochastic orders and their applications, Academic, New York, 1994.
29. M. Shaked and T. Wong, Stochastic orders based on ratios of Laplace transforms, J Appl Probab 34 (1997), 404-419.
30. J.G. Shanthikumar and D.D. Yao, The preservation of likelihood ratio ordering under convolutions, Stochastic Process Appl 23 (1986), 259-267.
31. R. Szekli, Stochastic ordering and dependence in applied probability, Springer-Verlag, New York, 1995.
32. S.S. Wang and V.R. Young, Ordering risks: Expected utility theory versus Yaari's dual theory of risk, Insurance Math Econom 22 (1998), 145-161.