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First off, let me be specific as to what I mean by "Benford's Law analysis": I'm looking to test, given some data, if the set of first significant digits are independent, identically distributed Benford random variables. As such, I would prefer the following:

  • The order in which the data is presented matters e.g. the data is in chronological order.
  • Reasonable expectation that the first significant digits might be IID.

Thus, for instance, doing this particular analysis on some sequence of population growth (1000 one year, 2000 the next, 4000 the year after that, etc.) would not be helpful, as certainly we would not expect those first significant digits to be independent of each other.

The only thing that comes to mind that meets the parameters I have set would be a chronologically ordered sequence of withdrawals/transactions from an account. But then how to obtain such data? I sure hope this question doesn't come across as lazy.

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Below is a short list of data sites that may be useful for this purpose. This list is not a comprehensive list by any means. Not all of the data on these sites will be chronological, but I think there are many datasets in these few sites that could be useful for testing Benford's.

http://testingbenfordslaw.com/

https://www.gapminder.org/data/

https://www.theguardian.com/data

https://www.data.gov/

https://www.kaggle.com/datasets

https://www.ncdc.noaa.gov/data-access

Also, using Google's new Dataset Search yield's a bunch of interesting tests with links to the datasets.

https://toolbox.google.com/datasetsearch

Aside from the above, the general form for using Benford's Law is:

$P(d) = log_b(d+1) - log_b(d) = log_b(1 + \frac1d)$

For other number bases $b$ where $b\geq1$ in case you wanted to test it on a dataset that is not decimal. The number set satisfies Benford's if the leading digit $d$ $(d \in \{1, ..., b-1\})$ occurs according to the general form.

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