Abstract

Decomposition of overlapping peaks is one of the most commonly used computer-enhanced procedures of instrumental analytical chemistry which is usually performed by nonlinear fitting a predefined model to the measured data. The minimum of the squared norm of the residuals between the model and the measured data is commonly served as a measure of goodness of fit. However, the minimum does not guarantee a unique solution of the fitting. Also confidence interval radii of the estimated model parameters are often overestimated. To solve these problems we have developed a new method of determining the uncertainty (named the undetectable perturbations (UPs) method) of the correlated peak parameters based on a predetermined norm of the residuals. A multiple band-decomposition procedure based on the variation of the initial peak parameters was chosen to guarantee the unique solution with a minimal uncertainty. The fluorescence spectra of solutions of fluorescein, trans-stilbene and benzene were decomposed. The polynomial modified Gaussians (PMG), weighted sum of Lorentzian and PMG; double asymmetrical sigmoid and asymmetrical log-normal functions were used as the models. The estimated model parameters were constrained by the values which had physical meaning. The confidence intervals of the asymmetrical peak parameters were evaluated using the linear approximation, the bootstrap and the UPs methods. It was found that the linear approximation and the bootstrap methods often overestimated radii of the confidence intervals. Use the Ups method allowed us to control the radii according to a predetermined level of the squared norm of the residuals as opposed to the common methods. Mathematical and physical justifications of the evaluated model parameters were discussed.

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