Stigler's approach to recovering the distribution of first significant digits in natural data sets

Joanne Lee, Wendy K. Tam Cho and George Judge ()

Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series from Department of Agricultural & Resource Economics, UC Berkeley

Abstract: In 1881, Newcomb conjectured that the first significant digits (FSDs) of numbers in statistical tables would follow a logarithmic distribution with the digit “1” occurring most often. However, because Newcomb’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 “Benford’s Law.” In the mid-1940s, Stigler claimed Benford’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.

Keywords: Benford’s Law; Stigler’s Law; Power Law; Maximum Entropy; Distance Measures (search for similar items in EconPapers)
Date: 2009-01-19
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Related works:
Journal Article: Stigler's approach to recovering the distribution of first significant digits in natural data sets (2010)
Working Paper: Stigler's approach to recovering the distribution of first significant digits in natural data sets (2009)
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