I have a distribution, which I initially assumed to be a Rayleigh, but it almost certainly isn't. Before I consider convolutions of various distributions, e.g. Rayleigh convolved with Boltzmann, Rayleigh convolved with Gaussian and so on, I was hoping someone with a good eye might be able to identify it:

[![enter image description here](https://i.stack.imgur.com/3O7CN.png)](https://i.stack.imgur.com/3O7CN.png) 

I have plotted the data with a Rayleigh on top of it to illustrate that it is somewhat similar but clearly this isn't the distribution.

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I've been asked to provide a little more information about the data. The data itself are fit residuals from a freqeuncy spectrum. The units of the residuals are in $\rm{dBV\_{pk}}$, the definition of which is $\rm{dBV\_{pk}} = 10\log\_{10}(V^{2}\_{pk})$.

I have converted the residuals from $\rm{dBV\_{pk}}$ to $V^{2}\_{pk}$ by $V^{2}\_{pk} = 10^{\rm{dBV\_{pk}} / 10}$ and this is what is shown in the histogram.

I initially assumed a Rayleigh as the original spectrum is an FFT, which transforms a signal with real and imaginary parts (both of which are Gaussian distributed) and the absolute value of the FFT is taken, which is exactly how a Rayleigh is produced.

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I again will add some further details outlining my motivation. 

I have some FFT spectra, which I know the general lineshape of. I want to get an understanding on the noise that is on top of the lineshape, so I look at the fit residuals. The idea being that if I know how the residuals of a spectra are distributed, I can then add it to the lineshape model for simulation purposes. I don't want to add my noise in logorithmic units, i.e. $\rm{dBV\_{pk}}$, it is preferable to do this in $V\_{pk}^{2}$.

The data I have provided are the residuals from 64 spectra, each having 801 residual points.

I can of course just perform a KDE of this and use this for simulation but it is nice to understand where this profile comes from. For example if one has flat white noise in the frequency domain, and convert this to linear units this is absolutely a Rayleigh distribution -- emerging because the real and imaginary parts of the signal are Gaussian distributed and one always takes the absolute magnitude of a resultant FFT -- Rayleigh!! 

I would like to find a similar argument flow for this case.

Data available here: <https://filebin.net/17y3un9vs1kh5cq0>