Some notions of multivariate positive dependence

Insurance: Mathematics and Economics

Volumn 37, Issue 1 SPEC. ISS., 2005, Pages 13-26

  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

Affiliation; Conditionally increasing; Conditionally increasing in sequence; Left corner set decreasing; Left tail decreasing; Left tail decreasing in sequence; Lower orthant decreasing ratio order; Multivariate total positivity of order two; Right corner set increasing; Right tail increasing; Right tail increasing in sequence; Upper orthant increasing order ratio

Indexed keywords

EID: 23444445156     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2004.09.004     Document Type: Article

References (24)

1. Ahmed, A.-H. N., Langberg, N.A., Leon, R.V., Proschan, F., 1978. Two Concepts of Positive Dependence with Applications in Multivariate Analysis. Technical Report M486, Department of Statistics, Florida State University, Tallahassee, FL.
2. J. Avérous J.-L. Dortet-Bernadet LTD and RTI dependence orderings The Canadian Journal of Statistics 28 2000 151-157
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 T.H. Savits M. Shaked A concept of negative dependence using stochastic ordering Statistics and Probability Letters 3 1985 81-86
5. H.W. Block M.L. Ting Some concepts of multivariate dependence Communications in Statistics A - Theory and Methods 10 1982 749-762
6. T.C. Christofides E. Vaggelatou A connection between supermodular ordering and positive/negative association Journal of Multivariate Analysis 88 2004 138-151
7. Colangelo, A., Scarsini, M., Shaked, M., 2005. Some positive dependence stochastic orders. Journal of Multivariate Analysis, to appear.
8. G. Dall'Aglio Fréchet classes and compatibility of distribution functions in: Proceedings of the Symposia Mathematica vol. IX Convegno di Calcolo delle Probabilità, INDAM, Rome, 1971 1972 Academic Press London
9. N. Ebrahimi M. Ghosh Multivariate negative dependence Communications in Statistics A - Theory and Methods 10 1981 307-337
10. J.D. Esary F. Proschan Relationships among some concepts of bivariate dependence The Annals of Mathematical Statistics 43 1972 651-655
11. J.D. Esary F. Proschan D.W. Walkup Association of random variables with applications The Annals of Mathematical Statistics 38 1967 1466-1474
12. R. Harris A multivariate definition for increasing hazard rate distribution functions The Annals of Mathematical Statistics 41 1970 713-717
13. Hollander, M., Proschan, F., Sconing, J. (1990). Information, censoring, and dependence. In: H.W., Block, A.R., Sampson, T.H., Savits, (Eds.), Topics in Statistical Dependence, IMS Lecture Notes-Monograph Series 16, Hayward, CA, pp. 257-268.
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 Journal of Multivariate Analysis 10 1980 467-498
16. G. Kimeldorf A.R. Sampson Positive dependence orderings Annals of the Institute of Statistical Mathematics 39 1987 113-128
17. G. Kimeldorf A.R. Sampson A framework for positive dependence Annals of the Institute of Statistical Mathematics 41 1989 31-45
18. M.-L.T. Lee Dependence by total positivity The Annals of Probability 13 1985 572-582
19. E.L. Lehmann Some concepts of dependence The Annals of Mathematical Statistics 37 1966 1137-1153
20. P.R. Milgrom R.J. Weber A theory of auctions and competitive bidding Econometrica 50 1982 1089-1122
21. A. Müller M. Scarsini Some remarks on the supermodular order Journal of Multivariate Analysis 73 2000 107-119
22. A. Müller M. Scarsini Stochastic comparison of random vectors with a common copula Mathematics of Operations Research 26 2001 723-740
23. A. Müller D. Stoyan Comparison Methods for Stochastic Models and Risks 2002 Wiley New York
24. F. Pellerey P. Semeraro A positive dependence notion based on the supermodular order 2003 Quaderni del Dipartimento del Politecnico di Torino Torino, Italy