The Inverse Gamma Distribution and Benford's Law

  • Rebecca F. Durst Williams College
  • Chi Huynh Georgia Institute of Technology
  • Adam Lott University of Rochester
  • Steven J. Miller Williams College
  • Eyvindur A. Palsson Virginia Tech
  • Wouter Touw Netherlands Cancer Institute
  • Gert Vriend Radboud University Medical Centre
Keywords: Benford's law; inverse gamma distribution; digit bias; Poisson summation


According to Benford's Law, many data sets have a bias towards lower leading digits (about 30% are 1's). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing in competitive sports. There are many common distributions that exhibit such bias, i.e. they are almost Benford.

These include the exponential and the Weibull distributions. Motivated by these examples and the fact that the underlying distribution of factors in protein structure follows an inverse gamma distribution, we determine the closeness of this distribution to a Benford distribution as its parameters change.

Author Biographies

Steven J. Miller, Williams College

Steven J. Miller is the corresponding author.

Wouter Touw, Netherlands Cancer Institute

Current email address is

How to Cite
Durst, R. F., Huynh, C., Lott, A., Miller, S. J., Palsson, E. A., Touw, W., & Vriend, G. (2020). The Inverse Gamma Distribution and Benford’s Law. The PUMP Journal of Undergraduate Research, 3, 95-109. Retrieved from