Benford's law, also called the first-digit law, first digit phenomenon, or
leading digit phenomenon, states that in lists of numbers from many real-life
sources of data, the digit 1 occurs almost one-third of the time, much greater
than the expected 11.1% (i.e., one digit out of 9). The increasingly larger numbers
occur less frequency as they grow in magnitude, to the point that 9 is the first digit
less than one time in twenty. This counter-intuitive result applies to a wide variety
of figures, including electricity bills, street addresses, stock prices, population numbers,
death rates, lengths of rivers, physical and mathematical constants.
It is named after physicist Frank Benford, who stated it in 1938.
It had been previously stated by Simon Newcomb in 1881.
The first rigorous formulation and proof was made by Theodore Hill in 1988.
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