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> in any random sample of numbers To be more precise: > Benford's law tends to apply most accurately to data that span several orders of magnitude. As a rule
by whack 7y ago
> in any random sample of numbers
To be more precise:
> Benford's law tends to apply most accurately to data that span several orders of magnitude. As a rule of thumb, the more orders of magnitude that the data evenly covers, the more accurately Benford's law applies. For instance, one can expect that Benford's law would apply to a list of numbers representing the populations of UK settlements. But if a "settlement" is defined as a village with population between 300 and 999, then Benford's law will not apply
https://en.wikipedia.org/wiki/Benford%27s_law#Explanations https://en.wikipedia.org/wiki/Benford%27s_law#Explanations
- jsweojtj 7y agoEven this explanation is incorrect. Evenly sampled data across many orders of magnitude give an even distribution of leading numbers. See my comment for code here: https://news.ycombinator.com/item?id=21541264 https://news.ycombinator.com/item?id=21541264 There are many distributions which do lead to the distribution of leading digits that follow Benford's law, just not uniform. Nor "uniform over several orders of magnitude".
- deleted 7y ago[deleted]
- whack 7y ago> Thus, real-world distributions that span several orders of magnitude rather uniformly They mean uniformly on a log distribution. Ie, there are a uniform number of elements between 10^x and 10^(x+1), for many different values of x. This is best shown by the graph here: https://en.wikipedia.org/wiki/Benford%27s_law#Overview https://en.wikipedia.org/wiki/Benford%27s_law#Overview