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

Implementation

An implementation (Java) due to Sedgewick and Wayne (search for Benford's law).

Go to the Dictionary of Algorithms and Data Structures home page.

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

Entry modified Mon Dec 19 11:09:22 2005.
HTML page formatted Mon Dec 19 14:07:46 2005.

Cite this as:
Paul E. Black, "Benford's law", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
http://www.nist.gov/dads/HTML/benfordslaw.html