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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.

Abstract

Benford's Law can be seen as one of the many first significant digit (FSD) distributions in a family of monotonically decreasing distributions. We examine the interrelationship between Benford and other monotonically decreasing distributions such as those arising from Stigler, Zipf, and the power laws. We examine the theoretical basis of the Stigler distribution and extend his reasoning by incorporating FSD first-moment information into information-theoretic methods. We present information-theoretic methods as a way to describe, connect, and unify these related distributions and thereby extend the reach of Benford's Law and FSD research more generally.

Suggested Citation

  • Lee, Joanne & Cho, Wendy K. Tam & Judge, George G., 2010. "Stigler's approach to recovering the distribution of first significant digits in natural data sets," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 82-88, January.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:2:p:82-88
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    1. Tam Cho, Wendy K. & Gaines, Brian J., 2007. "Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance," The American Statistician, American Statistical Association, vol. 61, pages 218-223, August.
    2. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 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. Rodriguez R.J., 2004. "First Significant Digit Patterns From Mixtures of Uniform Distributions," The American Statistician, American Statistical Association, vol. 58, pages 64-71, February.
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    1. Henry, Miguel & Mittelhammer, Ron & Loomis, John, 2018. "An Information-Theoretic Approach to Estimating Willingness To Pay for River Recreation Site Attributes," MPRA Paper 89842, University Library of Munich, Germany.
    2. Hürlimann, Werner, 2015. "On the uniform random upper bound family of first significant digit distributions," Journal of Informetrics, Elsevier, vol. 9(2), pages 349-358.
    3. Henry-Osorio, Miguel & Mittelhammer, Ronald C., 2012. "An Information-Theoretic Approach to Modeling Binary Choices: Estimating Willingness to Pay for Recreation Site Attributes," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 123432, Agricultural and Applied Economics Association.

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