Talk:Benford's law

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Dispersion should not be too small[edit]

normally never mentioned: the dispersion or variance should be not "to small". A kind of proof in nordisk Matematisk tidskrift from 1965 ( or almost) has that condition included in teh proof. —Preceding unsigned comment added by 130.226.230.8 (talkcontribs) 16:18, 16 May 2008

Phone numbers as a non-Benford's Law distribution[edit]

The article currently gives "the 1974 Vancouver, Canada telephone book" as an example of a distribution that does not obey Benford's Law since "no number [in it] began with the digit 1". However, in the North American Numbering Plan (obeyed by Canada), telephone numbers are never allowed to begin with 1. I feel this example should be removed or, at the very least, this fact should be noted in a footnote. Admiral.Mercurial (talk) 12:47, 30 August 2014 (UTC)

  • @Admiral.Mercurial: I agree that's an error in Raimi (the original paper notes 0 incidence of 1s but doesn't investigate it) and we should probably remove the claim. Protonk (talk) 13:42, 30 August 2014 (UTC)
  • Thanks for catching this. If it's an error in the original paper (and not an introduced Wikipedia error), it would be better to explain the error, with a Wikilink to the North American Numbering Plan. Simply removing the erroneous claim leaves open the possibility of it being re-added, or of it misleading a reader who follows the footnote to the original paper. Reify-tech (talk) 13:57, 31 August 2014 (UTC)
I'm not sure it's an error. Rather it's a trivial example with an obvious explanation.--Jack Upland (talk) 00:21, 1 September 2014 (UTC)
It may be obvious to us here and now, but evidently it wasn't obvious and trivial to the authors of the paper at the time of writing, since they noticed it but offered no explanation for the anomaly. I think it is better to explain it as an example of inadvertent bias, rather than to omit it as "obvious", when it was clearly not obvious to the authors of the paper. It still remains non-obvious to readers unfamiliar with the North American Numbering Plan. Reify-tech (talk) 13:29, 1 September 2014 (UTC)
I agree with Jack. It is not an error, it is a trivial example with an obvious explanation. The authors of the paper apparently found it too obvious to even mention. But there's nothing wrong with saying it explicitly, so I just added it. :-D --Steve (talk) 14:01, 1 September 2014 (UTC)
I must say this example seems really silly: it is like saying that the numbers in the 20s violate Benford's law. GeneCallahan (talk) 16:32, 2 October 2016 (UTC)
I agree. It is silly. Even if the phone numbers were allowed to begin with the digit 1, the distribution would not be Benford because numbers are not distributed logarithmicly. Constant314 (talk) 18:03, 2 October 2016 (UTC)

Benford's Law in Nuclear Physics[edit]

Benford's law is applicable for the evaluated nuclear physics quantities. It works reasonably well for large samples (>400) and performs poorly for a small sample (~12). These results have been published in Journal Of Physics G [1]. It is a first application of Benford's law in nuclear physics.

  1. ^ B Pritychenko 2015 J. Phys. G: Nucl. Part. Phys. 42 075103. doi:10.1088/0954-3899/42/7/075103

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Special case of Zipf's Law?[edit]

In the introduction section, it states that Benford's law is a special case of Zipf's law. However, the citation is a dead link, and as someone already marked, clarification is needed since the naive interpretation of it being a special case (that the first digit frequencies follow a power law) is obviously false. On the Zipf's law page, some connection to Benford's law is briefly discussed, but I find this still unclear.

The only citation in that part (apart from the same dead link) does not claim that Benford is a special case of Zipf; the closest it gets is: "In this sense, it is interesting to explore also connections with other well known scale invariant features such as the Zipf’s law" [1]. Perhaps what is really meant is that Benford's law is a corollary of Zipf's law, if we assume that the probability distribution of numbers follows a power law.

In the meantime, I suggest we simply say (rather vaguely) that it has been argued that this law is related to Zipf's law as they both come from scale invariance.

Gneisss (talk) 21:43, 20 September 2017 (UTC)

I agree on all counts and I like your proposed edit. --Steve (talk) 11:59, 21 September 2017 (UTC)