Testing Benford’s Law with the first two significant digits

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dc.contributor.authorWong, Stanley Chun Yu
dc.contributor.supervisorLesperance, M. L.
dc.date.accessioned2010-09-07T16:31:20Z
dc.date.available2010-09-07T16:31:20Z
dc.date.copyright2010en
dc.date.issued2010-09-07T16:31:20Z
dc.degree.departmentDept. of Mathematics and Statisticsen
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractBenford’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.en
dc.identifier.urihttp://hdl.handle.net/1828/3031
dc.languageEnglisheng
dc.language.isoenen
dc.rightsAvailable to the World Wide Weben
dc.subjectsignificant digiten
dc.subjectgoodness-of-fit testen
dc.subjectlikelihood ratio testen
dc.subjectCramѐr-von Misesen
dc.subjectsimultaneous confidence intervalen
dc.subject.lcshUVic Subject Index::Sciences and Engineering::Mathematics::Mathematical statisticsen
dc.titleTesting Benford’s Law with the first two significant digitsen
dc.typeThesisen

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