Multivariate extreme value theory : Models and estimation

2005 Fiscal Year Final Research Report Summary

• Project/Area Number: 16500174
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Kobe University
• Principal Investigator: TAKAHASHI Rinya Kobe University, Faculty of Maritime Sciences, Professor, 海事科学部, 教授 (80030047)
• Co-Investigator(Kenkyū-buntansha): SIBUYA Masaaki Takachiho University, Faculty of Commercial Sciences, Professor, 商学部, 教授 (20146723)
• Project Period (FY): 2004 – 2005
• Keywords: extreme value theory / multivariate extreme value distribution / statistical model / data analysis / dependence measure / 従属性 / 上位r個

Research Abstract

1.In multivariate extreme value data analysis, the methods of using the upper r largest data and the power transformation of the marginal data were studied. We showed that these methods were efficient for estimating the marginal distributions of the multivariate extreme value distributions.
2.Dependence among components of the multivariate extreme value distributions was characterized by its spectrum measure or by its exponent measure. A dependence order based on stable tail dependence function was introduced. The implication of the order in the risk theory was discussed.

Research Products

• [Journal Article] 火災損害額データの解析 (2005)
  • Author(s): 高橋 倫也
  • Journal Title: アクチュアリージャーナル 16巻・57号 Pages: 1-19
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Extreme value analysis of the fire claims data. (In Japanese.) (2005)
  • Author(s): Takahashi, R.
  • Journal Title: Actuary Journal 16-57 Pages: 1-19
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] The shapes of the probability density, hazard, and reverse hazard functions. (2005)
  • Author(s): Sibuya, M
  • Journal Title: Advance on Models, Characterizations and Applications.(Balakrishnan, N., Bairamov, I.G.and Gebizlioglu, O.L.(Eds))(Chapman, Hall, Boca Raton, FL) Pages: 1-18
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Equivalence of partial and conditional correlation coefficients. (2004)
  • Author(s): Baba, K.
  • Journal Title: Journal of the Japan Statistical Society. 35・1 Pages: 1-20
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Equivalence of partial and conditional correlation coefficients. (2004)
  • Author(s): Baba, K.
  • Journal Title: Journal of the Japan Statistical Society 35-1 Pages: 1-20
  • Description: 「研究成果報告書概要(欧文)」より
• [Book] The shapes of the probability density, hazard, and reverse hazard functions. Balakrishnan, N., Bairamov, I. G. and Gebizlioglu, O. L. (Eds), Advance on Models, Characterizations and Applications. (2005)
  • Author(s): Sibuya, M.
  • Total Pages: 1-19.
  • Publisher: Chapman Hall, Boca Raton
  • Description: 「研究成果報告書概要(和文)」より