The space of D-norms revisited

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• 作者：Stefan Aulbach (1)
  Michael Falk (1)
  Maximilian Zott (1)
  
  1. Institute of Mathematics ; University of W眉rzburg ; Emil-Fischer-Str. 30 ; 97074 ; W眉rzburg ; Germany
  
• 关键词：Multivariate extreme value theory ; Max ; stable distributions ; D ; norm ; Generator of D ; norm ; Doubly stochastic matrix ; Dirichlet distribution ; Dirichlet D ; norm ; Primary鈥?0G70 ; Secondary鈥?0E99
• 刊名：Extremes
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：18
• 期：1
• 页码：85-97
• 全文大小：245 KB
• 参考文献：1. Balakrishnan, N, Basu, AP (1996) Exponential Distribution: Theory, Methods and Applications. CRC Press, Boca Raton
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Quality Control, Reliability, Safety and Risk
  Civil Engineering
  Hydrogeology
  Environmental Management
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer U.S.
• ISSN：1572-915X

文摘

The theory of D-norms is an offspring of multivariate extreme value theory. We present recent results on D-norms, which are completely determined by a certain random vector called generator. In the first part it is shown that the space of D-norms is a complete separable metric space, if equipped with the Wasserstein-metric in a suitable way. Secondly, multiplying a generator with a doubly stochastic matrix yields another generator. An iteration of this multiplication provides a sequence of D-norms and we compute its limit. Finally, we consider a parametric family of D-norms, where we assume that the generator follows a symmetric Dirichlet distribution. This family covers the whole range between complete dependence and independence.