One of the historical and fundamental uses of the Edgeworth and Gram-Charlier series is to “correct” a Gaussian density when it is determined that the probability density under consideration has moments that do not correspond to the Gaussian [5, 6]. There is a fundamental difficulty with these methods in that if the series are truncated, then the resulting approximate density is not manifestly positive. The aim of this paper is to attempt to expand a probability density so that if it is truncated it will still be manifestly positive.
L. Cohen, L. Cohen,
"Series approximation to probability densities", Proc. SPIE 10648, Automatic Target Recognition XXVIII, 106480C (30 April 2018); doi: 10.1117/12.2304808; https://doi.org/10.1117/12.2304808