×

zbMATH — the first resource for mathematics

Supermodular dependence ordering on a class of multivariate copulas. (English) Zbl 1005.60037
The authors find various sets of conditions on pairs of extensions of Archimedean copulas, under which the copulas are ordered in the supermodular stochastic order.

MSC:
60E15 Inequalities; stochastic orderings
62E10 Characterization and structure theory of statistical distributions
PDF BibTeX Cite
Full Text: DOI
References:
[1] Bäuerle, N., Inequalities for stochastic models via supermodular orderings, Comm. statist. stochastic models, 13, 181-201, (1997) · Zbl 0871.60015
[2] Bäuerle, N.; Müller, A., Modeling and comparing dependencies in multivariate risk portfolios, ASTIN bull., 28, 59-76, (1998) · Zbl 1137.91484
[3] Bäuerle, N.; Rieder, U., Comparison results for Markov-modulated recursive models, Probab. eng. inform. sci., 11, 203-217, (1997) · Zbl 1096.60518
[4] Beneš, V.; Stěpán, J., Distributions with given marginals and moment problems, (1997), Kluwer Academic Publishers Dordrecht
[5] Dall’Aglio, G., Kotz, S., Salinetti, G. (Eds.) 1991. Advances in Probability Distributions with Given Marginals. Kluwer Academic Publishers, Dordrecht.
[6] Galambos, J., The asymptotic theory of extreme order statistics, (1987), Kreiger Publishing Co Malabar, FL · Zbl 0634.62044
[7] Goovaerts, M.J.; Dhaene, J., Supermodular ordering and stochastic annuities, Insurance math. econom., 24, 281-290, (1999) · Zbl 0942.60008
[8] Hu, T.; Pan, X., Comparisons of dependence for stationary Markov processes, Probab. eng. inform. sci., 14, 299-315, (2000) · Zbl 0974.60076
[9] Joe, H., Multivariate concordance, J. multivariate anal., 35, 12-30, (1990) · Zbl 0741.62061
[10] Joe, H., Families of MIN-stable multivariate exponential and multivariate extreme value distributions, Statist. probab. lett., 9, 75-81, (1990) · Zbl 0686.62035
[11] Joe, H., Multivariate models and dependence concepts, (1997), Chapman & Hall London · Zbl 0990.62517
[12] Kemperman, J.H.B., On the FKG-inequalities for measures on a partially ordered space, Proc. akad. wetenschappen. ser. A, 80, 313-331, (1977) · Zbl 0384.28012
[13] Lorentz, G.C., An inequality for rearrangements, Amer. math. monthly, 60, 176-179, (1953) · Zbl 0050.28201
[14] Meester, L.E.; Shanthikumar, J.G., Regularity of stochastic processes, Probab. eng. inform. sci., 7, 343-360, (1993)
[15] Müller, A., Stop-loss order for portfolios of dependent risks, Insurance math. econom., 21, 219-223, (1997) · Zbl 0894.90022
[16] Müller, A.; Scarsini, M., Some remarks on the supermodular order, J. multivariate anal., 73, 107-119, (2000) · Zbl 0958.60009
[17] Nelsen, R.B., An introduction to copulas, (1999), Springer New York · Zbl 0909.62052
[18] Resnick, S.I., Extreme values, regular variation, and point processes, (1987), Springer New York · Zbl 0633.60001
[19] Rüschendorf, L.; Schweizer, B.; Taylor, M.D., Distributions with fixed marginals and related topics, (1996), IMS Hayward, CA
[20] Shaked, M.; Shanthikumar, J.G., Supermodular stochastic orders and positive dependence of random vectors, J. multivariate anal., 61, 86-101, (1997) · Zbl 0883.60016
[21] Tchen, A.H., Inequalities for distributions with given marginals, Ann. probab., 8, 814-827, (1980) · Zbl 0459.62010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.