Fractional Divergence of Probability Densities

The divergence or relative entropy between probability densities is examined. Solutions that minimise the divergence between two distributions are usually “trivial” or unique. By using a fractional-order formulation for the divergence with respect to the parameters, the distance between probability densities can be minimised so that multiple non-trivial solutions can be obtained. As a result, the fractional divergence approach reduces the divergence to zero even when this is not possible via the conventional method. This allows replacement of a more complicated probability density with one that has a simpler mathematical form for more general cases.