The modified three point Gaussian method for determining Gaussian peak parameters

A modified three point Gaussian (MTPG) method for analyzing histogrammed peaks which are assumed to have an underlying Gaussian distribution has been developed. The original three point Gaussian method introduces systematic biases in estimating area A and full-width at half maximum (FWHM) of Gaussian peaks in histogrammed spectra, in addition to resulting in relatively large uncertainties in these estimates. This bias is caused by choosing the midpoint of each bin as the x-coordinate when calculating the three parameters of a Gaussian distribution (A, centroid μ, and FWHM). The MTPG method applied an iterative procedure to more accurately determine the x-coordinate for each bin used in three point Gaussian method. In the FWHM range of about 0.5–2 bins, the MTPG method converged after several iterations (typically 5 to 6), in the process eliminating the bias introduced by the original method. Additionally, the uncertainties of A and FWHM estimates in this same FWHM range were minimized and approached the statistical limits. A detailed description of the MTPG method and results over a range of peak areas and FWHMs are presented.