메뉴 건너뛰기




Volumn 88, Issue 1, 2004, Pages 138-151

A connection between supermodular ordering and positive/negative association

Author keywords

Convex order; Increasing convex order; Kolmogorov type inequalities; Positive and negative association; Rosenthal inequalities; Supermodular order

Indexed keywords


EID: 0346973100     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(03)00064-2     Document Type: Article
Times cited : (125)

References (29)
  • 1
    • 0010007351 scopus 로고
    • Positive dependence in multivariate distributions
    • K. Alam, K.M.L. Saxena, Positive dependence in multivariate distributions, Comm. Statist. Theor. Methods A 10 (1981) 1183-1196.
    • (1981) Comm. Statist. Theor. Methods A , vol.10 , pp. 1183-1196
    • Alam, K.1    Saxena, K.M.L.2
  • 2
    • 0000727196 scopus 로고    scopus 로고
    • Inequalities for stochastic models via supermodular orders
    • N. Bäuerle, Inequalities for stochastic models via supermodular orders, Comm. Statist. Stochastic Models 13 (1997) 181-201.
    • (1997) Comm. Statist. Stochastic Models , vol.13 , pp. 181-201
    • Bäuerle, N.1
  • 3
    • 85011531647 scopus 로고    scopus 로고
    • Modelling and comparing dependencies in multivariate risk portfolios
    • N. Bäuerle, A. Müller, Modelling and comparing dependencies in multivariate risk portfolios, ASTIN Bull. 28 (1998) 59-76.
    • (1998) ASTIN Bull. , vol.28 , pp. 59-76
    • Bäuerle, N.1    Müller, A.2
  • 5
    • 0036612670 scopus 로고    scopus 로고
    • On the distance between convex-ordered random variables, with applications
    • M.V. Boutsikas, E. Vaggelatou, On the distance between convex-ordered random variables, with applications, Adv. Appl. Probab. 34 (2002) 349-375.
    • (2002) Adv. Appl. Probab. , vol.34 , pp. 349-375
    • Boutsikas, M.V.1    Vaggelatou, E.2
  • 6
    • 0013439051 scopus 로고
    • Rearrangement inequalities
    • P.W. Day, Rearrangement inequalities, Canad. J. Math. 24 (1972) 930-943.
    • (1972) Canad. J. Math. , vol.24 , pp. 930-943
    • Day, P.W.1
  • 7
    • 0000681044 scopus 로고    scopus 로고
    • Does positive dependence between individual risks increase stop-loss premiums?
    • M. Denuit, J. Dhaene, C. Ribas, Does positive dependence between individual risks increase stop-loss premiums?, Insurance Math. Econom. 28 (2001) 305-308.
    • (2001) Insurance Math. Econom. , vol.28 , pp. 305-308
    • Denuit, M.1    Dhaene, J.2    Ribas, C.3
  • 8
    • 0041970176 scopus 로고    scopus 로고
    • Smooth generators of integral stochastic orders
    • M. Denuit, A. Müller, Smooth generators of integral stochastic orders, Ann. Appl. Probab. 12 (2002) 1174-1184.
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 1174-1184
    • Denuit, M.1    Müller, A.2
  • 9
    • 0001382704 scopus 로고
    • Association of random variables with applications
    • J.D. Esary, F. Proschan, D. Walkup, Association of random variables with applications, Ann. Math. Statist. 38 (1967) 1466-1474.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1466-1474
    • Esary, J.D.1    Proschan, F.2    Walkup, D.3
  • 10
    • 0001007372 scopus 로고
    • Subadditive functions on a distributive lattice and an extension of Szász's inequality
    • K. Fan, Subadditive functions on a distributive lattice and an extension of Szász's inequality, J. Math. Anal. Appl. 18 (1967) 262-268.
    • (1967) J. Math. Anal. Appl. , vol.18 , pp. 262-268
    • Fan, K.1
  • 11
    • 0346754596 scopus 로고    scopus 로고
    • Negatively superadditive dependence of random variables with applications
    • T. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probab. Statist. 16 (2000) 133-144.
    • (2000) Chinese J. Appl. Probab. Statist. , vol.16 , pp. 133-144
    • Hu, T.1
  • 12
    • 0000709793 scopus 로고
    • Negative association of random variables, with applications
    • K. Joag-Dev, F. Proschan, Negative association of random variables, with applications, Ann. Statist. 11 (1983) 286-295.
    • (1983) Ann. Statist. , vol.11 , pp. 286-295
    • Joag-Dev, K.1    Proschan, F.2
  • 13
    • 24844444362 scopus 로고    scopus 로고
    • Comparison of sequences of dependent random variables using supermodular order with applications
    • preprint
    • R. Kulik, R. Szekli, Comparison of sequences of dependent random variables using supermodular order with applications, 2002, preprint.
    • (2002)
    • Kulik, R.1    Szekli, R.2
  • 14
    • 0043233777 scopus 로고    scopus 로고
    • The Hàjeck-Rényi inequality for the NA random variables and its application
    • J. Liu, S. Gan, P. Chen, The Hàjeck-Rényi inequality for the NA random variables and its application, Statist. Probab. Lett. 43 (1999) 99-105.
    • (1999) Statist. Probab. Lett. , vol.43 , pp. 99-105
    • Liu, J.1    Gan, S.2    Chen, P.3
  • 15
    • 0003428399 scopus 로고
    • Inequalities: Theory of Majorization and its Applications
    • Academic Press, New York
    • A.W. Marshall, I. Olkin, Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979.
    • (1979)
    • Marshall, A.W.1    Olkin, I.2
  • 16
    • 0000571327 scopus 로고
    • A note on the almost sure convergence of sums of negatively associated random variables
    • P. Matula, A note on the almost sure convergence of sums of negatively associated random variables, Statist. Probab. Lett. 15 (1992) 209-213.
    • (1992) Statist. Probab. Lett. , vol.15 , pp. 209-213
    • Matula, P.1
  • 17
    • 84976015324 scopus 로고
    • Regularity of stochastic processes: A theory of directional convexity
    • L.E. Meester, J.G. Shanthikumar, Regularity of stochastic processes: a theory of directional convexity, Probab. Eng. Inform. Sci. 7 (1993) 343-360.
    • (1993) Probab. Eng. Inform. Sci. , vol.7 , pp. 343-360
    • Meester, L.E.1    Shanthikumar, J.G.2
  • 18
    • 0031574502 scopus 로고    scopus 로고
    • Stop loss order for portfolios of dependent risks
    • A. Müller, Stop loss order for portfolios of dependent risks, Insurance Math. Econom. 21 (1998) 219-223.
    • (1998) Insurance Math. Econom. , vol.21 , pp. 219-223
    • Müller, A.1
  • 19
    • 6644229355 scopus 로고    scopus 로고
    • Stochastic ordering of multivariate Normal distribution
    • A. Müller, Stochastic ordering of multivariate Normal distribution, Ann. Inst. Statist. Math. 53 (2001) 567-575.
    • (2001) Ann. Inst. Statist. Math. , vol.53 , pp. 567-575
    • Müller, A.1
  • 20
    • 0001312122 scopus 로고    scopus 로고
    • Some remarks on the supermodular order
    • doi:10.1006/jmva.1999.1873
    • A. Müller, M. Scarsini, Some remarks on the supermodular order, J. Multivariate Anal. 73 (2000) 107-119 doi:10.1006/jmva.1999.1873.
    • (2000) J. Multivariate Anal. , vol.73 , pp. 107-119
    • Müller, A.1    Scarsini, M.2
  • 21
    • 0003900086 scopus 로고    scopus 로고
    • Comparison Methods for Stochastic Models and Risks
    • Wiley, Chichester
    • A. Müller, D. Stoyan, Comparison Methods for Stochastic Models and Risks, Wiley, Chichester, 2002.
    • (2002)
    • Müller, A.1    Stoyan, D.2
  • 22
    • 51249187914 scopus 로고
    • p(p>2) spanned by sequences of independent random variables
    • p(p>2) spanned by sequences of independent random variables, Israel J. Math. 8 (1970) 273-303.
    • (1970) Israel J. Math. , vol.8 , pp. 273-303
    • Rosenthal, H.P.1
  • 23
    • 0003445519 scopus 로고
    • Stochastic Orders and their Applications
    • Academic Press, New York
    • M. Shaked, J.G. Shanthikumar, Stochastic Orders and their Applications, Academic Press, New York, 1994.
    • (1994)
    • Shaked, M.1    Shanthikumar, J.G.2
  • 24
    • 0002949510 scopus 로고    scopus 로고
    • Supermodular stochastic orders and positive dependence of random vectors
    • doi:10.1006/jmva.1997.1656
    • M. Shaked, J.G. Shanthikumar, Supermodular stochastic orders and positive dependence of random vectors, J. Multivariate Anal. 61 (1997) 86-101 doi:10.1006/jmva.1997.1656.
    • (1997) J. Multivariate Anal. , vol.61 , pp. 86-101
    • Shaked, M.1    Shanthikumar, J.G.2
  • 25
    • 0034559111 scopus 로고    scopus 로고
    • A comparison theorem on moment inequalities between negatively associated and independent random variables
    • Q.M. Shao, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theor. Probab. 13 (2000) 343-356.
    • (2000) J. Theor. Probab. , vol.13 , pp. 343-356
    • Shao, Q.M.1
  • 26
    • 0346719558 scopus 로고    scopus 로고
    • Moment inequalities and weak convergence for negatively associated sequences
    • C. Su, L.C. Zhao, Y.B. Wang, Moment inequalities and weak convergence for negatively associated sequences, Sci. China A 40 (1997) 172-182.
    • (1997) Sci. China A , vol.40 , pp. 172-182
    • Su, C.1    Zhao, L.C.2    Wang, Y.B.3
  • 27
    • 0003313363 scopus 로고
    • Stochastic Ordering and Dependence in Applied Probability
    • Springer, Berlin
    • R. Szekli, Stochastic Ordering and Dependence in Applied Probability, in: Lecture notes in Statistics, Vol. 97, Springer, Berlin, 1995.
    • (1995) Lecture Notes in Statistics , vol.97
    • Szekli, R.1
  • 28
    • 0000925325 scopus 로고
    • Inequalities for distributions with given marginals
    • A.H. Tchen, Inequalities for distributions with given marginals, Ann. Probab. 8 (1980) 814-827.
    • (1980) Ann. Probab. , vol.8 , pp. 814-827
    • Tchen, A.H.1
  • 29
    • 0000348040 scopus 로고
    • Minimizing a submodular function on a lattice
    • D.M. Topkis, Minimizing a submodular function on a lattice, Oper. Res. 26 (1978) 305-321.
    • (1978) Oper. Res. , vol.26 , pp. 305-321
    • Topkis, D.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.