  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 data
should be uncorrelated with the acquired signal. The developed statistical
method was evaluated using computer simulated spectra. The numerical
estimations of the calculated parameter applying this method, indicate an
improvement over accuracy and precision, being one order of magnitude better
than those produced by least squares approaches. We still have to evaluate the
improvement produced by this method over Detection and Quantitation Limits, in
TXRF spectral analysis.
