"Non ideal" Lorentzians I am not sure if this is a question about math, physics or electrical engineering... Anyway, I am currently trying to analyze some measurement data. What I have is essentially the transmissivity (i.e. S21 using EE terminology) for a high-Q resonator (Q value about 10^6). Ideally a resonator of this type should have a shape that is very nearly Lorentzian. However, what we see is that the shape depends on the temperature and at elevated temperatures s clearly "distorted" , we believe there is a rather interesting reason for this temperature dependence (meaning it is worth looking into). Now, I would like to somehow "quantify" this change to that I can plot it as a function of temperature. Is there a generally accepted way to quantify how much the shape of a resonance deviates from an ideal Lorentzian? I seem to remember seeing something similar, i.e. a "shape factor" (not the same thing as the shape factor in EE), being used in atomic spectroscopy but I can't find anything useful using Google schoolar.