Undergraduate thesis, Williams College, Williamstown, Massachusetts .

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

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**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