q-Gaussian Tsallis Line Shapes and Raman Spectral Bands

q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, range 1 < 3, q-functions pass from usual Gaussian form, for close to 1, that a heavy tailed distribution, at 3. The value q=2 corresponds Cauchy-Lorentzian distribution. This behavior q-Gaussian functions could be interesting specific application, regarding analysis Raman spectra, where Lorentzian and profiles line shapes most used fit spectral bands. Therefore, we will propose with aim comparing resulting data available literature. As it clear discussion, this very sensitive issue. We also provide detailed discussion about Voigt pseudo-Voigt role shape modeling show successfully comparison these q-Gaussians. EPR spectroscopy (Howarth et al., 2003), given as