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Optimization Letters

, Volume 6, Issue 1, pp 99–125 | Cite as

Copulas with maximum entropy

  • Julia PiantadosiEmail author
  • Phil Howlett
  • Jonathan Borwein
Original Paper

Abstract

We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration. Finally, we discuss the numerical calculations for some hypothetical examples and describe how this work can be applied to the modelling and simulation of monthly rainfall.

Keywords

Copula Maximum entropy Grade correlation Fenchel duality 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Julia Piantadosi
    • 1
    Email author
  • Phil Howlett
    • 1
  • Jonathan Borwein
    • 2
  1. 1.School of Mathematics and Statistics, CIAMUniversity of South AustraliaMawson LakesAustralia
  2. 2.School of Mathematical and Physical Sciences, CARMAThe University of NewcastleCallaghanAustralia

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