Benford's law

(definition)

Definition: On a wide variety of statistical data, the first digit is d with the probability log₁₀ ( 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 log₁₀ ( 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

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 26 August 2008.
HTML page formatted Wed Mar 13 12:42:45 2019.

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