Benford’s Law states that the first significant digit for most data is not uniformly distributed. Instead, it follows the distribution: P(d = d1) = log10(1 + 1/d1) for d1 ϵ {1, 2, …, 9}. In 2006, my supervisor, Dr. Mary Lesperance et. al tested the goodness-of-fit of data to Benford’s Law using the first significant digit. Here we extended the research to the first two significant digits by performing several statistical tests – LR-multinomial, LR-decreasing, LR-generalized Benford, LR-Rodriguez, Cramѐr-von Mises Wd2, Ud2, and Ad2 and Pearson’s χ2; and six simultaneous confidence intervals – Quesenberry, Goodman, Bailey Angular, Bailey Square, Fitzpatrick and Sison.
When testing compliance with Benford’s Law, we found that the test statistics LR-generalized Benford, Wd2 and Ad2 performed well for Generalized Benford distribution, Uniform/Benford mixture distribution and Hill/Benford mixture distribution while Pearson’s χ2 and LR-multinomial statistics are more appropriate for the contaminated additive/multiplicative distribution. With respect to simultaneous confidence intervals, we recommend Goodman and Sison to detect deviation from Benford’s Law.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/3031 |
| Date | 07 September 2010 |
| Creators | Wong, Stanley Chun Yu |
| Contributors | Lesperance, M. L. |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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