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Wong, SCY (2010)

Testing Benfordís Law with the first two significant digits

Master's Thesis, University of Victoria, Canada.

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



Abstract: Benfordís 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, Ö, 9}. In 2006, my supervisor, Dr. Mary Lesperance et. al tested the goodness-of-fit of data to Benfordís Law using the first significant digit. Here we extended the research to the first two significant digits by performing several statistical tests Ė LR-multinomial, LR-decreasing, LR-generalized Benford, LR-Rodriguez, Cramѐr-von Mises Wd2, Ud2, and Ad2 and Pearsonís χ2; and six simultaneous confidence intervals Ė Quesenberry, Goodman, Bailey Angular, Bailey Square, Fitzpatrick and Sison. When testing compliance with Benfordís 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 Pearsonís 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 Benfordís Law.


Bibtex:
@mastersThesis{, AUTHOR = {Wong, Stanley Chun Yu}, TITLE = {Testing Benfordís 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