Sometimes spectral peaks are fitted using a very pathological function named the Lorentz/Cauchy distribution. The Lorentz distribution has the property of not having a defined mean nor standard deviation.
Is this methodology adequate? What does it mean to have a lorentzian? Is there a criterion based on the nature of the spectra to prefer a Lorentzian instead of a Gaussian ?
I would tend to think that with a distribution like that it is hard to define the energy of the peak as it has a big probability of having photons that arrive with very high/low energy. Also without standard deviation how you characterize the width? Does this have any more physical implications?
Edit: I think a more concise question would be: should I interpret the (lorentzian) spectrum as probability distribution of having a number of photon per unit of energy?