The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration

Modern chromatographic data acquisition softwares often behave as black boxes where the researchers have little control over the raw data processing. One of the significant interests of separation scientists is to extract physico-chemical information from chromatographic experiments and peak parameters. In addition, column developers need the total peak shape analysis to characterize the flow profile in chromatographic beds. Statistical moments offer a robust approach for providing detailed information for peaks in terms of area, its center of gravity, variance, resolution, and its skew without assuming any peak model or shape. Despite their utility and theoretical significance, statistical moments are rarely incorporated as they often provide underestimated or overestimated results because of inappropriate choice of the integration method and selection of integration limits. The Gaussian model is universally used in most chromatography softwares to assess efficiency, resolution, and peak position. Herein we present a user-friendly, and accessible approach for calculating the zeroth, first, second, and third moments through more accurate numerical integration techniques (Trapezoidal and Simpson's rule) which provide an accurate estimate of peak parameters as compared to rectangular integration. An Excel template is also provided which can calculate the four moments in three steps with or without baseline correction.