I'm a geologist working with some sparse borehole data. The boreholes sample igneous intrusions and we're trying to fit a distribution to the thickness of the intrustion vs frequency (for use in other models).

I'm using scipy stats to fit a range of distributions, and the one that has the highest K-S score is a lognormal distribution (p=0.7). The data is definitely skewed, so needs a skewed distribution? However, when plotting the log transformed data, the distribution fit doesn't 'look' particularly good:

enter image description here

I was wondering if any of the experts on here could quickly eyeball if a log-normal distrubution is appropriate here, and if not then advise on what we should be using.

The only other published data similar to this shows a similar distribution of thickness-frequency (albeit, magnitude of thickness differs for geological reasons). I've asked the author for their data, but their histogram is here:

enter image description here

I'd appreciate thoughts, but also will just say that we can't get more data as the data we're using was acquired by various oil companies, and is very expensive to acquire so we are kind of stuck with what we've got! We have less data (n=58) than the published histogram.

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    $\begingroup$ Can you explain more about "we're trying to fit a distribution to the thickness of the intrustion vs frequency (for use in other models)." Generally, the distribution of the raw data is unimportant, if the goal is to fit a regression model to the data. $\endgroup$ – Robert Long Jan 8 at 17:48
  • $\begingroup$ Hi sorry for the slow reply over the weekend. The distribution of the thickness data is being used in a Monte Carlo style workflow after this, so it's how best to fit a distribution to the data for that. $\endgroup$ – 8556732 Jan 11 at 13:35

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