메뉴 건너뛰기




Volumn 32, Issue 1, 2008, Pages 3-35

Construction of multivariate distributions: A review of some recent results

Author keywords

Associated random variables; Conditionally specified distributions; Mixture distributions; Multivariate weighted distributions; Multivariate Zipf distributions; Order statistics; Rosenblatt transformation; Skew distributions; Variables in common; Vines

Indexed keywords


EID: 47749109804     PISSN: 16962281     EISSN: 20138830     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (58)

References (92)
  • 3
    • 0040647877 scopus 로고
    • The multivariate Poisson-lognormal distribution
    • Aitchison, J. and Ho, C. H. (1989). The multivariate Poisson-lognormal distribution. Biometrika, 76, 4, 643-653.
    • (1989) Biometrika , vol.76 , Issue.4 , pp. 643-653
    • Aitchison, J.1    Ho, C.H.2
  • 4
    • 0004231080 scopus 로고
    • International Co-operative Publishing House, Fairland, MD
    • Arnold, B. C. (1983). Pareto Distributions. International Co-operative Publishing House, Fairland, MD.
    • (1983) Pareto Distributions
    • Arnold, B.C.1
  • 7
    • 0036619050 scopus 로고    scopus 로고
    • Skewed multivariate models related to hidden truncation and/or selective reporting
    • with discussion
    • Arnold, B. C. and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion). Test, 11, 7-54.
    • (2002) Test , vol.11 , pp. 7-54
    • Arnold, B.C.1    Beaver, R.J.2
  • 8
    • 0042454700 scopus 로고
    • Identifiability for dependent multiple decrement/competing risk models
    • Arnold, B. C. and Brockett, P. L. (1983). Identifiability for dependent multiple decrement/competing risk models. Scandinavian Actuarial Journal, 10, 117-127.
    • (1983) Scandinavian Actuarial Journal , vol.10 , pp. 117-127
    • Arnold, B.C.1    Brockett, P.L.2
  • 12
    • 84986604770 scopus 로고    scopus 로고
    • Conditionally specified distributions: An introduction
    • with discussion
    • Arnold, B. C., Castillo, E. and Sarabia, J. M. (2001). Conditionally specified distributions: an introduction (with discussion), Statistical Science, 16, 249-274.
    • (2001) Statistical Science , vol.16 , pp. 249-274
    • Arnold, B.C.1    Castillo, E.2    Sarabia, J.M.3
  • 13
    • 30944439133 scopus 로고    scopus 로고
    • Conditionally specified multivariate skewed distributions
    • Arnold, B. C., Castillo, E. and Sarabia, J. M. (2002). Conditionally specified multivariate skewed distributions. Sankhya, Ser. A, 64, 1-21.
    • (2002) Sankhya, Ser. A , vol.64 , pp. 1-21
    • Arnold, B.C.1    Castillo, E.2    Sarabia, J.M.3
  • 15
    • 34249724996 scopus 로고    scopus 로고
    • Distributions with generalized skewed conditionals and mixtures of such distributions
    • DOI 10.1080/03610920601125862, PII 779066062
    • Arnold, B. C., Castillo, E. and Sarabia, J. M. (2007a). Distributions with generalized skewed conditionals and mixtures of such distributions. Communications in Statistics, Theory and Methods, 36, 1493-1503. (Pubitemid 46828379)
    • (2007) Communications in Statistics - Theory and Methods , vol.36 , Issue.8 , pp. 1493-1503
    • Arnold, B.C.1    Castillo, E.2    Sarabia, J.M.3
  • 18
    • 0000193946 scopus 로고
    • Bivariate distributions with conditionals in prescribed exponential families
    • Arnold, B. C. and Strauss, D. (1991). Bivariate distributions with conditionals in prescribed exponential families, Journal of the Royal Statistical Society, Ser. B, 53, 365-375.
    • (1991) Journal of the Royal Statistical Society, Ser. B , vol.53 , pp. 365-375
    • Arnold, B.C.1    Strauss, D.2
  • 19
    • 19744373319 scopus 로고    scopus 로고
    • The skew-normal distribution and related multivariate families
    • Azzalini, A. (2005). The skew-normal distribution and related multivariate families. Scandinavian Journal of Statistics, 32, 159-188.
    • (2005) Scandinavian Journal of Statistics , vol.32 , pp. 159-188
    • Azzalini, A.1
  • 20
    • 0001417140 scopus 로고    scopus 로고
    • The multivariate skew-normal distribution
    • Azzalini,A. andDalla Valle,A. (1996). The multivariate skew-normal distribution. Biometrika, 83, 715-726.
    • (1996) Biometrika , vol.83 , pp. 715-726
    • Azzalini, A.1    Dalla Valle, A.2
  • 22
    • 0037900005 scopus 로고    scopus 로고
    • Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution
    • DOI 10.1111/1467-9868.00391
    • Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society, Ser. B, 65, 367-389. (Pubitemid 36607794)
    • (2003) Journal of the Royal Statistical Society. Series B: Statistical Methodology , vol.65 , Issue.2 , pp. 367-389
    • Azzalini, A.1    Capitanio, A.2
  • 23
    • 11144259051 scopus 로고    scopus 로고
    • Discussion of "Skewed multivariate models related to hidden truncation and/or selective reporting", by B. C. Arnold and R. J. Beaver
    • Balakrishnan, N. (2002). Discussion of "Skewed multivariate models related to hidden truncation and/or selective reporting", by B. C. Arnold and R. J. Beaver. Test, 11, 37-39.
    • (2002) Test , vol.11 , pp. 37-39
    • Balakrishnan, N.1
  • 24
    • 84856512967 scopus 로고    scopus 로고
    • Discrete multivariate distributions
    • (Eds. J. L. Teugels and B. Sundt), John Wiley and Sons, New York
    • Balakrishnan, N. (2004). Discrete multivariate distributions. In: Encyclopedia of Actuarial Sciences (Eds. J. L. Teugels and B. Sundt), pp. 549-571. John Wiley and Sons, New York.
    • (2004) Encyclopedia of Actuarial Sciences , pp. 549-571
    • Balakrishnan, N.1
  • 25
    • 84856538205 scopus 로고    scopus 로고
    • Discrete multivariate distributions
    • 2nd ed. (Eds. N. Balakrishnan, C. Read and B. Vidakovic). John Wiley and Sons, New York
    • Balakrishnan, N. (2005). Discrete multivariate distributions. In: Encyclopedia of Statistical Sciences, 2nd ed. (Eds. N. Balakrishnan, C. Read and B. Vidakovic). John Wiley and Sons, New York.
    • (2005) Encyclopedia of Statistical Sciences
    • Balakrishnan, N.1
  • 26
    • 0031524138 scopus 로고    scopus 로고
    • Normal inverse Gaussian distributions and stochastic volatility modelling
    • Barndorff-Nielsen, O. E. (1997). Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics, 24, 1-13.
    • (1997) Scandinavian Journal of Statistics , vol.24 , pp. 1-13
    • Barndorff-Nielsen, O.E.1
  • 27
    • 0036392207 scopus 로고    scopus 로고
    • Vines - A new graphical model for dependent random variables
    • DOI 10.1214/aos/1031689016
    • Bedford, T. and Cooke, R. (2002). Vines-a new graphical model for dependent random variables. The Annals of Statistics, 30, 4, 1031-1068. (Pubitemid 37095337)
    • (2002) Annals of Statistics , vol.30 , Issue.4 , pp. 1031-1068
    • Bedford, T.1    Cooke, R.M.2
  • 28
    • 0035178888 scopus 로고    scopus 로고
    • A general class of multivariate skew-elliptical distributions
    • DOI 10.1006/jmva.2000.1960
    • Branco, M. D. and Dey, D. K. (2001). A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis, 79, 99-113. (Pubitemid 33082674)
    • (2001) Journal of Multivariate Analysis , vol.79 , Issue.1 , pp. 99-113
    • Branco, M.D.1    Dey, D.K.2
  • 34
    • 38649115683 scopus 로고    scopus 로고
    • Univariate and multivariate versions of the negative binomial inverse Gaussian distribution with applications
    • Gómez-Déniz, E., Sarabia, J. M. and Calderín-Ojeda, E. (2008). Univariate and multivariate versions of the negative binomial inverse Gaussian distribution with applications. Insurance: Mathematics and Economics, 42, 39-49.
    • (2008) Insurance: Mathematics and Economics , vol.42 , pp. 39-49
    • Gómez-Déniz, E.1    Sarabia, J.M.2    Calderín-Ojeda, E.3
  • 38
    • 13444257789 scopus 로고    scopus 로고
    • Generalized skew normal model
    • Gupta, R. C. and Gupta, R. D. (2004). Generalized skew normal model. Test, 13, 501-524. (Pubitemid 40217253)
    • (2004) Test , vol.13 , Issue.2 , pp. 501-524
    • Gupta, R.C.1    Gupta, R.D.2
  • 39
    • 0011960461 scopus 로고
    • Some interrelations among compound and generalized distributions
    • Gurland, J. (1957). Some interrelations among compound and generalized distributions. Biometrika, 44, 265-268.
    • (1957) Biometrika , vol.44 , pp. 265-268
    • Gurland, J.1
  • 41
    • 0041611622 scopus 로고    scopus 로고
    • Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters
    • Distributions with fixed margins and related topics
    • Joe, H. (1996). Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In: Distributions with fixed margins and related topics, IMS Lecture Notes Monograph Series, 120-141.
    • (1996) IMS Lecture Notes Monograph Series , pp. 120-141
    • Joe, H.1
  • 43
    • 0030590937 scopus 로고    scopus 로고
    • A model for a multivariate binary response with covariates based on compatible conditionally specified logistic regressions
    • DOI 10.1016/S0167-7152(96)00021-1, PII S0167715296000211
    • Joe, H. and Liu, Y. (1996). A model for a multivariate binary response with covariates based on conditionally specified logistic regressions. Statistics and Probability Letters, 31, 113-120. (Pubitemid 126167284)
    • (1996) Statistics and Probability Letters , vol.31 , Issue.2 , pp. 113-120
    • Joe, H.1    Liu, Y.2
  • 45
    • 0037079675 scopus 로고    scopus 로고
    • A dependent bivariate t distribution with marginals on different degrees of freedom
    • Jones, M. C. (2002). A dependent bivariate t distribution with marginals on different degrees of freedom. Statistics and Probability Letters, 56, 163-170.
    • (2002) Statistics and Probability Letters , vol.56 , pp. 163-170
    • Jones, M.C.1
  • 46
    • 11144322968 scopus 로고    scopus 로고
    • Families of distributions arising from distributions of order statistics
    • with discussion
    • Jones, M. C. (2004). Families of distributions arising from distributions of order statistics (with discussion), Test, 13, 1-43.
    • (2004) Test , vol.13 , pp. 1-43
    • Jones, M.C.1
  • 47
    • 11144306061 scopus 로고    scopus 로고
    • Multivariate distributions with support above the diagonal
    • DOI 10.1093/biomet/91.4.975
    • Jones, M. C. and Larsen, P. V. (2004). Multivariate distributions with support above the diagonal. Biometrika, 91, 975-986. (Pubitemid 41388931)
    • (2004) Biometrika , vol.91 , Issue.4 , pp. 975-986
    • Jones, M.C.1    Larsen, P.V.2
  • 49
    • 0039193154 scopus 로고
    • Interrelations among generalized distributions and their components
    • Katti, S. K. (1966). Interrelations among generalized distributions and their components. Biometrics, 22, 44-52.
    • (1966) Biometrics , vol.22 , pp. 44-52
    • Katti, S.K.1
  • 50
    • 49849095960 scopus 로고
    • Bivariate Hermite distributions
    • Kemp, C. D. and Papageorgiou, H. (1982). Bivariate Hermite distributions. Sankhya, Ser. A, 44, 269-280.
    • (1982) Sankhya, Ser. A , vol.44 , pp. 269-280
    • Kemp, C.D.1    Papageorgiou, H.2
  • 56
    • 84856540222 scopus 로고    scopus 로고
    • Constructions of discrete bivariate distributions
    • Birkhäuser, Boston., N. Balakrishnan, E. Castillo, J.M. Sarabia Editors
    • Lai, C. D. (2006). Constructions of discrete bivariate distributions. In: Advances on Distribution Theory, Order Statistics and Inference, Birkhäuser, Boston., N. Balakrishnan, E. Castillo, J.M. Sarabia Editors, 29-58.
    • (2006) Advances on Distribution Theory, Order Statistics and Inference , pp. 29-58
    • Lai, C.D.1
  • 57
    • 0002388693 scopus 로고    scopus 로고
    • Properties and applications of the Sarmanov family of bivariate distributions
    • Lee, M.-L. T. (1996). Properties and applications of the Sarmanov family of bivariate distributions. Communications in Statistics, Theory and Methods, 25, 1207-1222.
    • (1996) Communications in Statistics, Theory and Methods , vol.25 , pp. 1207-1222
    • Lee, M.-L.T.1
  • 60
    • 33751542466 scopus 로고    scopus 로고
    • Copulas: Tales and facts
    • Mikosch, T. (2006). Copulas: tales and facts. Extremes, 9, 3-20.
    • (2006) Extremes , vol.9 , pp. 3-20
    • Mikosch, T.1
  • 61
    • 33244471096 scopus 로고    scopus 로고
    • Multivariate weighted distributions: A review and some extensions
    • DOI 10.1080/02331880500439691, PII W172723628785612
    • Navarro, J., Ruiz, J. M. and Del Aguila, Y. (2006). Multivariate weighted distributions: a review and some extensions. Statistics, 40, 51-64. (Pubitemid 43279587)
    • (2006) Statistics , vol.40 , Issue.1 , pp. 51-64
    • Navarro, J.1    Ruiz, J.M.2    Del, A.Y.3
  • 64
    • 0037405514 scopus 로고    scopus 로고
    • A bivariate beta distribution
    • DOI 10.1016/S0167-7152(03)00048-8, PII S0167715203000488
    • Olkin, I. and Liu, R. (2003). A bivariate beta distribution. Statistics and Probability Letters, 62, 407-412. (Pubitemid 36439419)
    • (2003) Statistics and Probability Letters , vol.62 , Issue.4 , pp. 407-412
    • Olkin, I.1    Liu, R.2
  • 65
    • 11144331182 scopus 로고
    • Intermediate order statistics with applications to nonparametric estimation
    • Papadatos, N. (1995). Intermediate order statistics with applications to nonparametric estimation. Statistics and Probability Letters, 22, 231-238.
    • (1995) Statistics and Probability Letters , vol.22 , pp. 231-238
    • Papadatos, N.1
  • 66
    • 3843151446 scopus 로고    scopus 로고
    • EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed λ
    • Protassov, R. S. (2004). EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed λ. Statistics and Computing, 14, 67-77.
    • (2004) Statistics and Computing , vol.14 , pp. 67-77
    • Protassov, R.S.1
  • 67
    • 0013381161 scopus 로고
    • On discrete distributions arising out of methods of ascertainment
    • Rao, C. R. (1965). On discrete distributions arising out of methods of ascertainment. Sankhya Series A, 27, 311-324.
    • (1965) Sankhya Series A , vol.27 , pp. 311-324
    • Rao, C.R.1
  • 69
    • 84884797092 scopus 로고    scopus 로고
    • Discussion of "Skewed Multivariate Models Related to Hidden Truncation and/or Selective Reporting", by B. C. Arnold and R. J. Beaver
    • Sarabia, J. M. (2002). Discussion of "Skewed Multivariate Models Related to Hidden Truncation and/or Selective Reporting", by B. C. Arnold and R. J. Beaver. Test, 11, 49-52.
    • (2002) Test , vol.11 , pp. 49-52
    • Sarabia, J.M.1
  • 70
    • 84856522072 scopus 로고    scopus 로고
    • Bivariate distributions based on the generalized three-parameter beta distribution
    • Birkhäuser, Boston., N. Balakrishnan, E. Castillo, J. M. Sarabia Editors
    • Sarabia, J. M. and Castillo, E. (2006). Bivariate distributions based on the generalized three-parameter beta distribution. In: Advances on Distribution Theory, Order Statistics and Inference, Birkhäuser, Boston., N. Balakrishnan, E. Castillo, J. M. Sarabia Editors, 85-110.
    • (2006) Advances on Distribution Theory, Order Statistics and Inference , pp. 85-110
    • Sarabia, J.M.1    Castillo, E.2
  • 71
    • 25444505627 scopus 로고    scopus 로고
    • A class of conjugate priors for log-normal claims based on conditional specification
    • DOI 10.1111/j.1539-6975.2005.00133.x
    • Sarabia, J. M., Castillo, E., Gómez, E. and Vázquez, F. (2005). A class of conjugate priors for log-normal claims based on conditional specification. Journal of Risk and Insurance, 72, 479-495. (Pubitemid 41360298)
    • (2005) Journal of Risk and Insurance , vol.72 , Issue.3 , pp. 479-495
    • Sarabia, J.M.1    Castillo, E.2    Gomez-Deniz, E.3    Vazquez-Polo, F.J.4
  • 74
    • 85011463077 scopus 로고    scopus 로고
    • On the use of conditional specification models in claim count distributions: An application to bonus-malus systems
    • Sarabia, J. M., Gómez-Déniz, E. and Vázquez-Polo, F. (2004).On the use of conditional specification models in claim count distributions: an application to bonus-malus systems. ASTIN Bulletin, 34, 85-98.
    • (2004) ASTIN Bulletin , vol.34 , pp. 85-98
    • Sarabia, J.M.1    Gómez-Déniz, E.2    Vázquez-Polo, F.3
  • 76
    • 34248560994 scopus 로고    scopus 로고
    • A new class of bivariate distributions and its mixture
    • Sarhan, A. M. and Balakrishnan, N. (2007). A new class of bivariate distributions and its mixture. Journal of Multivariate Analysis, 98, 1508-1527.
    • (2007) Journal of Multivariate Analysis , vol.98 , pp. 1508-1527
    • Sarhan, A.M.1    Balakrishnan, N.2
  • 77
    • 2342593007 scopus 로고
    • Generalized normal correlation and two-dimensional Frechet classes
    • Sarmanov, O. V. (1966). Generalized normal correlation and two-dimensional Frechet classes. Doklady, Soviet Mathematics, 168, 596-599.
    • (1966) Doklady, Soviet Mathematics , vol.168 , pp. 596-599
    • Sarmanov, O.V.1
  • 78
    • 43049087091 scopus 로고    scopus 로고
    • Bivariate Student t distributions with variable marginal degrees of freedom and independence
    • In press
    • Shaw, W. T. and Lee, K. T. A. (2008). Bivariate Student t distributions with variable marginal degrees of freedom and independence. Journal of Multivariate Analysis, In press.
    • (2008) Journal of Multivariate Analysis
    • Shaw, W.T.1    Lee, K.T.A.2
  • 79
    • 0011299338 scopus 로고
    • On a family of discrete distributions particularly suited to represent long-tailed frequency data
    • Eds. N.F. Laubscher, Pretoria, South Africa: Council for Scientific and Industrial Research
    • Sichel, H. S. (1971). On a family of discrete distributions particularly suited to represent long-tailed frequency data. In: Proceedings of the third Symposium on Mathematical Statistics, Eds. N.F. Laubscher, Pretoria, South Africa: Council for Scientific and Industrial Research, 51-97.
    • (1971) Proceedings of the Third Symposium on Mathematical Statistics , pp. 51-97
    • Sichel, H.S.1
  • 80
  • 82
    • 80054925114 scopus 로고    scopus 로고
    • A class of multivariate discrete distributions based on an approximate density in GLMM
    • Tonda, T. (2005). A class of multivariate discrete distributions based on an approximate density in GLMM. Hiroshima Math. J., 35, 327-349.
    • (2005) Hiroshima Math. J. , vol.35 , pp. 327-349
    • Tonda, T.1
  • 83
    • 85011468696 scopus 로고    scopus 로고
    • On the bivariate generalized Poisson distribution
    • Vernic, R. (1997). On the bivariate generalized Poisson distribution. ASTIN Bulletin, 27, 23-31.
    • (1997) ASTIN Bulletin , vol.27 , pp. 23-31
    • Vernic, R.1
  • 84
    • 34848836979 scopus 로고    scopus 로고
    • A multivariate generalization of the generalized Poisson distribution
    • Vernic, R. (2000). A multivariate generalization of the generalized Poisson distribution. ASTIN Bulletin, 30, 57-67.
    • (2000) ASTIN Bulletin , vol.30 , pp. 57-67
    • Vernic, R.1
  • 85
    • 33644863485 scopus 로고    scopus 로고
    • Multivariate skew-normal distributions with applications in insurance
    • Vernic, R. (2005). Multivariate skew-normal distributions with applications in insurance. Insurance: Mathematics and Economics, 38, 413-426.
    • (2005) Insurance: Mathematics and Economics , vol.38 , pp. 413-426
    • Vernic, R.1
  • 87
    • 4043103972 scopus 로고    scopus 로고
    • A skew-symmetric representation of multivariate distributions
    • Wang, J., Boyer, J. and Genton, M. G. (2004). A skew-symmetric representation of multivariate distributions. Statistica Sinica, 14, 1259-1270. (Pubitemid 40131613)
    • (2004) Statistica Sinica , vol.14 , Issue.4 , pp. 1259-1270
    • Wang, J.1    Boyer, J.2    Genton, M.G.3
  • 88
    • 0030505288 scopus 로고    scopus 로고
    • A New conditional specification of the bivariate Poisson conditionals distribution
    • Wesolowski, J. (1996). A New conditional specification of the bivariate Poisson conditionals distribution. Statistica Neerlandica, 50, 390-393.
    • (1996) Statistica Neerlandica , vol.50 , pp. 390-393
    • Wesolowski, J.1
  • 90
    • 0037079667 scopus 로고    scopus 로고
    • Six multivariate Zipf distributions and their related properties
    • Yeh, H. C. (2002). Six multivariate Zipf distributions and their related properties. Statistics and Probability Letters, 56, 131-141.
    • (2002) Statistics and Probability Letters , vol.56 , pp. 131-141
    • Yeh, H.C.1
  • 91
    • 0348234106 scopus 로고    scopus 로고
    • Some properties and characterizations for generalized multivariate Pareto distributions
    • Yeh, H. C. (2004). Some properties and characterizations for generalized multivariate Pareto distributions. Journal of Multivariate Analysis, 88, 47-60.
    • (2004) Journal of Multivariate Analysis , vol.88 , pp. 47-60
    • Yeh, H.C.1
  • 92
    • 34147127020 scopus 로고    scopus 로고
    • Three general multivariate semi-Pareto distributions and their characterizations
    • Yeh, H. C. (2007). Three general multivariate semi-Pareto distributions and their characterizations. Journal of Multivariate Analysis, 98, 1305-1319.
    • (2007) Journal of Multivariate Analysis , vol.98 , pp. 1305-1319
    • Yeh, H.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.