Maximum likelihood and moment estimators for the voigt profile via Fourier transform

The Voigt profile is widely used to model experimental line broadening phenomena in physics. Because its density is available only in integral form, parameter estimation is typically based on non-linear least squares of the empirical Voigt profile. Exploiting a representation showing that the Dual Voigt distribution is a reflected truncated normal distribution we propose a purely statistical approach. This characterization enables parameter estimation by leveraging standard results for the truncated normal family. Examples with simulated data suggest that the proposed estimators achieve substantially lower mean squared error. These results highlight the advantages of a likelihood-based approach grounded in the probabilistic structure of the Dual Voigt model.