Editing Benford's law (section)

==History==
The discovery of Benford's law goes back to 1881, when the Canadian-American astronomer [[Simon Newcomb]] noticed that in [[logarithm table]]s the earlier pages (that started with 1) were much more worn than the other pages.<ref name=Newcomb>{{Cite journal | author = Simon Newcomb | s2cid = 124556624 | author-link = Simon Newcomb | title = Note on the frequency of use of the different digits in natural numbers | journal = [[American Journal of Mathematics]] | volume = 4 | issue = 1/4 | year = 1881 | pages = 39–40 | doi = 10.2307/2369148 | jstor = 2369148 | bibcode = 1881AmJM....4...39N }}</ref> Newcomb's published result is the first known instance of this observation and includes a distribution on the second digit as well. Newcomb proposed a law that the probability of a single number ''N'' being the first digit of a number was equal to log(''N''&nbsp;+&nbsp;1)&nbsp;−&nbsp;log(''N'').

The phenomenon was again noted in 1938 by the physicist [[Frank Benford]],<ref name=Benford/> who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of 335 rivers, the sizes of 3259 US populations, 104 [[physical constant]]s, 1800 [[molecular weight]]s, 5000 entries from a mathematical handbook, 308 numbers contained in an issue of ''[[Reader's Digest]]'', the street addresses of the first 342 persons listed in ''American Men of Science'' and 418 death rates. The total number of observations used in the paper was 20,229. This discovery was later named after Benford (making it an example of [[Stigler's law]]).

In 1995, [[Ted Hill (mathematician)|Ted Hill]] proved the result about mixed distributions mentioned [[#Multiple probability distributions|below]].<ref name=Hill1995/><ref name="Hill1995b">{{cite journal |last1=Hill |first1=Theodore P. |title=Base-invariance implies Benford's law |journal=Proceedings of the American Mathematical Society |volume=123 |issue=3 |year=1995 |pages=887–895 |issn=0002-9939 |doi=10.1090/S0002-9939-1995-1233974-8 |doi-access=free}}</ref>