About the Optimal Density Associated to the Chiral Index of a Sample from a Bivariate Distribution

The complex quadratic form where z is afixed vector in and z' is its transpose, and P is any permutation matrixs, is shown to be a convex combination of the quadratic forms where denotes the symmetric permuation matrices. We deduce that the optimal probability density associated to the chiral index of a sample from a bivariate distribution is symmetric. This result is used to locate the upper bound of the chiral index of any bivariate distribution in the interval

By: Don Coppersmith; Michel Petitjean

Published in: RC23464 in 2004


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