Stigler's approach to recovering the distribution of first significant digits in natural data sets
AbstractIn 1881, Newcomb conjectured that the first significant digits (FSDs) of numbers in statistical tables would follow a logarithmic distribution with the digit â€œ1â€ occurring most often. However, because Newcombâ€™s proposal was not presented with a theoretical basis, it was not given much attention. Fifty-seven years later, Benford argued for the same principle and showed it was relevant to a large range of data sets, and the logarithmic FSD distribution became known as â€œBenfordâ€™s Law.â€ In the mid-1940s, Stigler claimed Benfordâ€™s Law contained a theoretical inconsistency and supplied an alternative derivation for the distribution of FSDs. In this paper, we examine the theoretical basis of the Stigler distribution and extend his reasoning by incorporating FSD first moment information and information-theoretic methods.
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Bibliographic InfoPaper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt9745m98d.
Date of creation: 19 Jan 2009
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Benfordâ€™s Law; Stiglerâ€™s Law; Power Law; Maximum Entropy; Distance Measures;
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