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Regular Vines: Generation Algorithm and Number of Equivalence Classes

In: Dependence Modeling Vine Copula Handbook

Author

Listed:
  • Harry Joe

    (Department of Statistics, University of British Columbia, Canada)

  • Roger M. Cooke

    (Department of Mathematics, Delft University of Technology, The Netherlands)

  • Dorota Kurowicka

    (Department of Mathematics, Delft University of Technology, The Netherlands)

Abstract

A natural order for a regular vine on n variables is an assignment of indices to the variables such that variables indexed with j and j + 1 occur as conditioned variables in a node of tree j, j = 1,…,n−1. Regular vines V and U on n variables are equivalent if there is a permutation π ∈ n! such that π(V) = U. U and V are equivalent if and only if the regular vines in natural order corresponding to U and V are equivalent. The number of equivalence classes for regular vines is obtained by counting the number of equivalence classes for regular vines in natural order.

Suggested Citation

  • Harry Joe & Roger M. Cooke & Dorota Kurowicka, 2010. "Regular Vines: Generation Algorithm and Number of Equivalence Classes," World Scientific Book Chapters, in: Dorota Kurowicka & Harry Joe (ed.), Dependence Modeling Vine Copula Handbook, chapter 10, pages 219-231, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814299886_0010
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