Centroid and full-width at half maximum uncertainties of histogrammed data with an underlying Gaussian distribution-the moments method

The effect of approximating a continuous Gaussian distribution with histogrammed data are studied. The expressions for theoretical uncertainties in centroid and full-width at half maximum (FWHM), as determined by calculation of moments, are derived using the error propagation method for a histogrammed Gaussian distribution. The results are compared with the corresponding pseudo-experimental uncertainties for computer-generated histogrammed Gaussian peaks to demonstrate the effect of binning the data. It is shown that increasing the number of bins in the histogram improves the continuous distribution approximation. For example, a FWHM⩾9 and FWHM⩾12 bins are needed to reduce the pseudo-experimental standard deviation of FWHM to within ⩽5% and ⩽1%, respectively, of the theoretical value for a peak containing 10000 counts. In addition, the uncertainties in the centroid and FWHM as a function of peak area are studied. Finally, Sheppard´s correction is applied to partially correct for the binning effect