Gram-Charlier and Edgeworth-Cramér series in the characterization of chromatographic peaks

The Gram-Charlier and Edgeworth-Cramér series can be used for characterization of chromatographic peaks in routine analytical networks involving a microcomputer for data acquisition with a minicomputer for data processing. A method is presented for this application. Polynomial expressions are given for the expansion of these series up to the tenth order. Examples of characterization of chromatographic peaks with different asymmetry are presented. It is shown that the Edgeworth-Cramér series can be used successfully for evaluation of area, mean, variance, skewness, excess and third and fourth cumulant coefficients. Higher orders of expansions are needed as the asymmetry factor of the peak studied increases and as the orders of the statistical moments or the cumulant coefficients of interest increase. For peaks corresponding to an asymmetry factor of 1.7, an expansion order of five is needed in the calculation of skewness and excess; evaluation of the third and fourth cumulant coefficients requires an expansion order of eight.