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Near-Gaussian probability densities are common in many important physicalapplications. Here we develop an asymptotic expansion methodology for computingentropic functionals for such densities. The expansion proposed is a closerelative of standard perturbation expansions in quantum field theory. We givenovel results on the low-order effects of non-Gaussian even moments andasymmetry (e.g. skewness) on the entropy. The asymptotic expansion is also usedto define a best fit maximum entropy density given a set of observed low ordermoments. The maximum entropy density estimation technique consists simply ofthe solution of a small set of algebraic equations and is therefore morestraightforward numerically than classical maximum-entropy methods which relyon sophisticated convex optimization techniques.

Near-Gaussian entropic functional calculation and density estimation using an asymptotic series