MSc thesis, Universiteit Utrecht, The Netherlands.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: INTRODUCTION: Inspired by Benford and also by present-day mathematicians as Ted Hill and Peter Schatte, in this masters thesis Benfordís Law will be examined without clinging to base 10. Usually tests on the degree to which numbers satisfy Benfordís Law are only done with respect to base 10. If the frequencies of numbers are equal to the by Benford predicted values in this base, then the numbers are said to satisfy Benfordís Law. We will see that statements about the degree to which numbers satisfy Benfordís Law should be made with care. In some cases this degree depends on the base being used. It is possible that numbers of which the first-digits are distributed logarithmically with respect to base 10, are not distributed logarithmically with respect to base 20. In this case without mentioning the base a Dutchman, who is counting in base 10, will claim that these numbers follow Benfordís Law while a Maya, who is counting in base 20, would never do this. The Dutchman should formulate his claim as: these numbers satisfy Benfordís Law with respect to base 10. The same problem arises when only a finite number of significant digits are regarded, in that case the distribution of the digits can depend on the measuring units being used. If for example only the first significant digit is regarded, it is possible that a Dutchman and an American do not agree whether or not their frequencies are equal to the by Benford predicted values
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Reference Type: Thesis
Subject Area(s): Analysis, Probability Theory