On the nonuniqueness of discretization of two-dimensional probability distribution subject to the maximization of Shannon's entropy

The maximum entropy method has been successfully applied to a number of scientific and engineering disciplines. A special case of its particular usefulness is the discretization of two-dimensional distribution subject to the maximization of Shannon's entropy. Such a discretization scheme provides a means for deriving a Iow-order approximation of probability distribution for mixed-mode (continuous and discrete) multivariate data. The presence of special cases is shown where the maximum-entropy discretization of two-dimensional probability distribution is not unique.

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