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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?

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The Lorentzian line shape arises when the width of the peak is determined by homogeneous broadening. It isn't an arbitrary choice by overzealous curve fitters, that really is the expected shape of the curve. That's why it is used.

While it's true that formally the distribution has no mean or moments, this is something of a trifling objection. The distribution has a peak value and a half height width that are perfectly well defined and can be used to describe the spectral line.

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  • $\begingroup$ I would expect the width to change as you vary the scale (the size of your channels), is that the case? $\endgroup$ – Mauricio Oct 31 '17 at 8:50

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