Master's Thesis, University of Victoria, Canada.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: 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.
Bibtex:
@mastersThesis{,
AUTHOR = {Wong, Stanley Chun Yu},
TITLE = {Testing Benford’s Law with the first two significant digits},
SCHOOL = {University of Victoria},
ADDRESS = {British Columbia, Canada},
YEAR = {2010},
URL = {https://dspace.library.uvic.ca/handle/1828/3031},
}
Reference Type: Thesis
Subject Area(s): Statistics