A Gram-Charlier series is an expansion of a probability distribution in derivatives or orthogonal polynomials associated with a reference distribution. The Gram-Charlier A series uses the normal distribution and Hermite polynomials for a continuous random variable. The Gram-Charlier B series instead uses a Poisson distribution and finite differences for a discrete random variable (Cramér 1946).
Gram-Charlier expansions are related to, but distinct from, the Edgeworth series. In particular, Edgeworth's construction orders terms by their asymptotic dependence on sample size rather than solely by polynomial degree.
