Undergraduate thesis, Williams College, Williamstown, Massachusetts .
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: Many datasets and real-life functions exhibit a leading digit bias, where the rst digit base 10 of a number equals 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. It is especially applicable in today's world of `Big Data' and can be used for fraud detection to test data integrity, as most people are unaware of the phenomenon. The cardinal goal is often determining which datasets follow Benford's Law. We know that the decomposition of a finite stick based on a reiterative cutting pattern determined by a `nice' probability density function will tend toward Benford's Law. We extend the results of [1] to show that this is also true when the cuts are determined by a finite set of nice probability density functions. We further conjecture that when we apply the same exact cut at every level, as long as that cut is not equal to 0.5, the lengths of the subsegments will converge to a Benford distribution.
Bibtex:
@mastersThesis{,
AUTHOR = {Joy Jing},
TITLE = {Benford’s Law and Stick Decomposition},
SCHOOL = {Williams College},
YEAR = {2013},
ADDRESS ={Williamstown, Massachusetts},
TYPE = {Undergraduate Honors Thesis},
URL = {https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/st/JoyJing.pdf},
}
Reference Type: Thesis
Subject Area(s): Probability Theory