Stigler's approach to recovering the distribution of first significant digits in natural data sets
In 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.
|Date of creation:||19 Jan 2009|
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- Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
- David Giles, 2007.
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Applied Economics Letters,
Taylor & Francis Journals, vol. 14(3), pages 157-161.
- David E. Giles, 2005. "Benford’s Law and Naturally Occurring Prices in Certain ebaY Auctions," Econometrics Working Papers 0505, Department of Economics, University of Victoria.
- Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
- Grendar, Marian & Judge, George & Schechter, Laura, 2007. "An empirical non-parametric likelihood family of data-based Benford-like distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 429-438.
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