Improvement of the gram-charlier method in univariate case

摘要

The Gram-Charlier expansion calculates the probability density function (pdf) using as input terms the moments data to an order and concerns an expansion in terms of Hermite polynomials and a standardized Gaussian. Usually the random variable is standardize, i.e. with mean equal to zero and standard deviations (#delta#) equal to one. The data standardization is sometimes too restrictive and it is possible to regulate the standard deviation so that should not necessarly be related to the classic choice (i.e. #delta#=1).