Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, and PSG R.

PROBLEM1: Problem_Copula_Defined_by_Correlation_Coefficients
Maximize Entropy
subject to
Linearmulti  = correlation coefficients
Linearmulti  = 1  (constraints defining  5-dimensional hyper–matrix)
Box constraints
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Box constraints = Lower bounds of elements of hyper–matrix
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n=4

n=6

n=8

n=10

This case study considers optimization problem statement for building a checkerboard copula of a joint distribution, using a prior information about Spearman Rho rank correlation coefficients. An m-dimensional copula where m≥2, is a continuous, m -increasing, probability distribution function C:[0,1]^m→ [0,1] on the unit m-dimensional hyper-cube with uniform marginal distributions. A checkerboard copula is a distribution with a corresponding density c:[0,1]^m→ [0,∞) defined almost everywhere by a step function on an m-uniform subdivision of the hyper-cube. I.e., the checkerboard copula is a distribution defined by subdividing the hyper-cube into n^m identical small hyper-cubes with constant density on each one.

We  found checkerboard copulas with known Spearmans Rho coefficients (m=5 and n=4, 8,10 ).