Some positive dependence stochastic orders

Journal of Multivariate Analysis

Volumn 97, Issue 1, 2006, Pages 46-78

  Colangelo, Antonio ^a   Scarsini, Marco ^b   Shaked, Moshe ^c  

^a BOCCONI UNIVERSITY   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

^c University of Arizona   (United States)

Author keywords

Archimedean copula; Copula; Farlie Gumbel Morgenstern distributions; Fr chet classes and bounds; Left tail decreasing (LTD); Likelihood ratio order; Lower orthant decreasing ratio (lodr) order; Marshall Olkin distributions; Multivariate total positivity; Right tail increasing (RTI); Upper orthant increasing ratio (uoir) order

Indexed keywords

EID: 28044471391     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmva.2004.11.006     Document Type: Article

References (30)

1. J. Averous J.-L. Dortet-Bernadet LTD and RTI dependence orderings Canad. J. Statist. 28 2000 151-157
2. F. Baccelli A.M. Makowski Multidimensional stochastic ordering and associated random variables Oper. Res. 37 1989 478-487
3. R.E. Barlow F. Proschan Statistical Theory of Reliability and Life Testing, Probability Models 1975 Holt, Rinehart, and Winston New York
4. H.W. Block M.-L. Ting Some concepts of multivariate dependence. Commun. Statist. - Theory Methods A 10 1981 749-762
5. P. Capéraà A.-L. Fougères C. Genest A stochastic ordering based on a decomposition of Kendall's Tau V. Beneš J. Štěpán (Eds.) Distributions with given Marginals and Moment Problems 1997 Kluwer Boston 81-86
6. A. Colangelo, Some Studies in Positive Dependence, Ph.D. dissertation, Università Bocconi, 2005.
7. A. Colangelo, M. Scarsini, M. Shaked, Some multivariate positive dependence notions, Canad. J. Statist. 2005, to appear.
8. P. Collet F.J. López S. Martínez Order relations of measures when avoiding decreasing sets Statist. Probab. Lett. 65 2003 165-175
9. M. Dall'Aglio M. Scarsini Zonoids, linear dependence, and size-biased distributions on the simplex Adv. Appl. Probab. 35 2003 871-884
10. M. Denuit J. Dhaene C. Le Bailly de Tilleghem S. Teghem Measuring the impact of a dependence among insured lifelengths Belg. Actuarial Bull. 1 2001 18-39
11. N. Ebrahimi M. Ghosh Multivariate negative dependence Commun. Statist. - Theory Methods A 10 1981 307-337
12. M. Hollander, F. Proschan, J. Sconing, Information, censoring, and dependence, in: H.W. Block, A.R. Sampson, T.H. Savits (Eds.), Topics in Statistical Dependence, IMS Lecture Notes-Monograph Series, vol. 16, Hayward, CA, pp. 257-268.
13. T. Hu B.-E. Khaledi M. Shaked Multivariate hazard rate orders J. Multivariate Anal. 84 2003 173-189
14. H. Joe Multivariate Models and Dependence Concepts 1997 Chapman & Hall London
15. S. Karlin Y. Rinott Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions J. Multivariate Anal. 10 1980 467-498
16. G. Kimeldorf A.R. Sampson Positive dependence orderings Ann. Inst. Statist. Math. 39 1987 113-128
17. G. Kimeldorf A.R. Sampson A framework for positive dependence Ann. Inst. Statist. Math. 41 1989 31-45
18. S. Kotz, N. Balakrishnan, N.L. Johnson, Continuous Multivariate Distributions, Vol. 1: Models and Applications, Wiley, New York, 2000.
19. A.W. Marshall I. Olkin A multivariate exponential distribution J. Amer. Statist. Assoc. 62 1967 30-44
20. M.H. Metry A.R. Sampson A family of partial orderings for positive dependence among fixed marginal bivariate distributions G. Dall'Aglio S. Kotz G. Salinetti (Eds.) Advances in Probability Distributions with Given Marginals (Rome, 1990) 1991 Kluwer Dordrecht 129-138
21. A. Müller, M. Scarsini, Archimedean copulae and positive dependence, J. Multivariate Anal. 2005, to appear, doi:10.1016/ j.jmva.2004.04.003.
22. A. Müller D. Stoyan Comparison Methods for Stochastic Models and Risks 2002 Wiley New York
23. R.B. Nelsen An Introduction to Copulas 1999 Springer New York
24. L. Rüschendorf Stochastically ordered distributions and monotonicity of the OC-function of sequential probability ratio tests Math. Oper. Statist. Ser. Statist. 12 1981 327-338
25. B. Schweizer A. Sklar Probabilistic Metric Spaces 1983 North-Holland New York
26. M. Shaked J.G. Shanthikumar Stochastic Orders and Their Applications 1994 Academic Press Boston
27. M. Shaked J.G. Shanthikumar Supermodular stochastic orders and positive dependence of random vectors J. Multivariate Anal. 61 1997 86-101
28. M. Sklar Fonctions de répartition à n dimensions et leurs marges Publ. l'Inst. Statist. Univ. Paris 8 1959 229-231
29. R. Szekli R.L. Disney S. Hur MR/GI/1 queues with positively correlated arrival stream J. Appl. Probab. 31 1994 497-514
30. W. Whitt Multivariate monotone likelihood ratio and uniform conditional stochastic order J. Appl. Probab. 19 1982 695-701