I have a set of data which is recorded in a $\log_{10}$ scale. To be exact it is $dBV_{pk} = 20\log_{10}(V_{pk})$ units. If I plot the distribution of the logged data as a PDF I get the following:

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If I then linearise this data, so $10^{dBV_{pk}/20}$, and again plot the distribution I get the following:

enter image description here

To me this looks very much like the Rayleigh distribution -- it could be something else, but that is my best guess so far.

My question is: Given that the linear data is a Rayleigh distribution -- what is the $log_{10}$ transformation of a Rayleigh distribution? Or can anyone identify the distribution of the first plot (the original logged data)? If either is answered it automatically gives me the other.


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