An “ad-hoc” modified likelihood function applied to optimization of data analysis in atomic spectroscopy

Abstract In this paper we propose an “ad-hoc” construction of the Likelihood Function, in order to develop a data analysis procedure, to be applied in atomic and nuclear spectral analysis. The classical Likelihood Function was modified taking into account the underlying statistics of the phenomena studied, by the inspection of the residues of the fitting, which should behave with specific statistical properties. This new formulation was analytically developed, but the sought parameter should be evaluated numerically, since it cannot be obtained as a function of each one of the independent variables. For this simple numerical evaluation, along with the acquired data, we also should process many sets of external data, with specific properties — This new random data should be uncorrelated with the acquired signal. The statistical method developed was evaluated over computer simulated spectra and over an experimental example. The numerical evaluations of the calculated parameter applying this method, indicate an improvement in one order of magnitude over accuracy compared with those produced by least squares approaches. In the experimental application of this method, over the quantification of Mn in a spectrum of a IAEA’s sample (Proficiency Ring Test, PTXRFIAEA12), we found an improvement over the precision of the results. We still have to evaluate the improvement produced by this method over Detection and Quantitation Limits, in TXRF spectral analysis.