動態系統（二）
期末報告主題
A1094108 蔡翔宇
A1104124 賴政韋
2024.04/15
BENFORD'S LAW
• In 1881 Simon Newcomb observes, “That the ten digits do not
occur with equal frequency must be evident to any one making
use of logarithmic tables, and noticing how much faster the first
pages wear out than the last ones. The first significant dight is
oftener 1 than any other dight, and the frequency diminishes up
to 9.”
• He went on to conclude that the “law of frequency” of
significant digits (base 10) satisfies
• 𝑃𝑟𝑜𝑏(𝑓𝑖𝑟𝑠𝑡𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡𝑑𝑖𝑔ℎ𝑡 = 𝑑) = 𝑙𝑜𝑔10
−1
(1 + 𝑑 ), 𝑑 = 1, … , 9
Applications
• Accounting fraud detection
• Power of 2
• Fibonacci series
• The populations of all the countries
• Physical constants
References
• Khan Academy (2011). Vi and Sal talk about the mysteries of Benford's law | Logarithms |
Algebra II | Khan Academy. https://www.youtube.com/watch?v=6KmeGpjeLZ0 (2024.04/12)
• Khan Academy (2011). Benford's law explanation (sequel to mysteries of Benford's law) |
Algebra II | Khan Academy. https://www.youtube.com/watch?v=SZUDoEdjTzg (2024.04/12)
• Andrea Dai (2020). 這世界不隨機！談班佛定律（Benford's Law). https://medium.com/andreasdiscovery/這世界不隨機-談班佛定律-benfords-law-81bc34157057 (2024.04/12)