Benford's Law and Finite Sets of Probability Density Functions

Monday, May 6, 2013 at 1:00pm to 1:45pm

Bronfman Science Center, 106 18 Hoxsey St, Williamstown, MA 01267, USA

Benford's Law and Finite Sets of Probability Density Functions

Joy Jing '13

Mathematics and Statistics Department Thesis Defense

Abstract:  Many datasets and real-life functions exhibit a leading digit bias, where the first digit of a number is 1 not 11% of the time as we would expect if all digits were equally likely, but closer to 30% of the time. This phenomenon is known as Benford's Law, and has applications ranging from the detection of tax fraud to analyzing the Fibonacci sequence. The cardinal goal is often determining which datasets follow Benford's Law.  We prove that the decomposition of a finite stick based on a cutting pattern determined by a finite set of 'nice' probability density functions will tend toward Benford's Law.  We further conjecture that when we apply the same exact same cut at every level, the distribution of lengths will still follow Benford's Law.

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Mathematics & Statistics

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