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ลิงก์ที่น่าสนใจ => ลิงก์คณิตศาสตร์ => Topic started by: psaipetc on February 20, 2008, 09:26:54 AM

Title: Benford's Law
Post by: psaipetc on February 20, 2008, 09:26:54 AM's_law

Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one third of the time, and larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is the first digit less than one time in twenty. This is based on the observation that real-world measurements are generally distributed logarithmically, thus the logarithm of a set of real-world measurements is generally distributed uniformly.

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, and processes described by power laws (which are very common in nature). Even more counter-intuitively, the result holds regardless of the base in which the numbers are expressed, although the exact proportions of course change.

It is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881 in his paper "Note on the Frequency of Use of the Different Digits in Natural Numbers". The first rigorous formulation and proof appears to be due to Theodore P. Hill in 1988.[1]...