Honors Thesis, Williams College.

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

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**Abstract:** Benford’s Law describes the situation in which the frequency distribution of the first digits in a real-life data set does not follow a uniform distribution. Rather, the probability of a digit d occurring as the leading digit of a data point is the difference between d+1 and d on a logarithmic scale with base 10. This phenomenon has been regularly used by auditors as a tool to detect fraud. The bootstrap is a resampling method which can be used to estimate the sampling distribution of an estimator, first proposed by Efron in 1979 [Ef].
We apply the bootstrap method to find a way to reduce the number of data points required for effective fraud detection based on Benford’s Law. Oftentimes an auditor may not have access to all the data; a method using a subset of the data for fraud detection makes the auditor’s job possible and potentially saves both human and computational resources. We have found that assuming that a data set of size 5000 or more is either free of manipulation or a result of summing the original values and some values following either a normal distribution or a uniform distribution, we only require 5% of the data to detect potential data manipulation.

**Bibtex:**

```
@mastersThesis{,
AUTHOR = {Lu Yang},
TITLE = {Benford’s Law and Fraud Detection},
SCHOOL = {Williams College},
YEAR = {2014},
TYPE = {Undergraduate Honors Thesis},
URL = {https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/st/YangLu.pdf},
NOTE = {last accessed December 8, 2019},
}
```

**Reference Type:** Thesis

**Subject Area(s):** Accounting, Statistics