Copulas with maximum entropy |
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Authors: | Julia Piantadosi Phil Howlett Jonathan Borwein |
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Institution: | (1) School of Mathematics and Statistics, CIAM, Mawson Lakes Campus University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, 5095, Australia |
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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. |
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Keywords: | |
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