(definition)

**Definition:**
On a wide variety of statistical data, the first digit is d with the probability log_{10} ( 1 + 1/d ).

**See also**
*Zipf's law*, *Lotka's law*.

*Note:
This is also referred to as "the first-digit phenomenon." The general significant-digit law is that the first significant digits ddd... d occur with the probability log _{10} ( 1 + 1/ddd... d ). This law was first published by Simon Newcomb in 1881. It went unnoticed until Frank Benford, apparently unaware of Newcomb's paper, concluded the same law and published it in 1938, supported by huge amounts of data.*

Author: PEB

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Entry modified 26 August 2008.

HTML page formatted Tue Jan 16 10:34:44 2018.

Cite this as:

Paul E. Black, "Benford's law", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 26 August 2008. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/benfordslaw.html