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

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  • Lee, Joanne
  • Cho, Wendy K. Tam
  • Judge, George G
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    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.

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    Bibliographic Info

    Paper 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.

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    Date of creation: 19 Jan 2009
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    Handle: RePEc:cdl:agrebk:qt9745m98d

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    Keywords: Benford’s Law; Stigler’s Law; Power Law; Maximum Entropy; Distance Measures;

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Mittelhammer,Ron C. & Judge,George G. & Miller,Douglas J., 2000. "Econometric Foundations Pack with CD-ROM," Cambridge Books, Cambridge University Press, number 9780521623940, April.
    2. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
    3. 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.
    4. 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.
    5. 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.
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