Benford's Law - Mark J. Nigrini

Benford's Law by Mark J. Nigrini (Wiley, 2012)

The book is available at amazon.com

The book is available at wiley.com

My Facebook page is Benford’s Law by Mark Nigrini

The links to the data files for Benford’s Law (2012) are shown below the photos on this page.

Frank Albert Benford

Frank Albert Benford

Frank Albert Benford

Frank A. Benford, Jr. 1883-1948

Lunch with Harry Benford, son of Frank Benford. We are looking at my Benford’s Law dissertation. Ann Arbor, Michigan 1993.

Home of Frank Benford on Rugby Road, Schenectady, New York. Photo taken April 22, 1994.

Lunch with the Benford family, children and grandchildren. Harry Benford is holding my 1999 Benford’s Law book. Manchester, New Hampshire 2000.

Inside Frank Benford’s study, Rugby Road, Schenectady. Photo taken September 2003.

Benford’s Law authors. Vrije Universiteit 1994. Left to right, Pieter Allaart, Mark Nigrini, Ted Hill.

Mark Nigrini and Ralph A. Raimi. Joint workshop presentation, Ralph Raimi on the theory, and myself on the practical applications of Benford’s Law. Niagara Falls, November 1996.

Mark Nigrini and Ralph A. Raimi. Joint workshop presentation, Ralph Raimi on the theory, and myself on the practical applications of Benford’s Law. Niagara Falls, November 1996.

Meeting Steven J. Miller on March 28, 2008 for the first time.

Meeting Steven J. Miller on March 28, 2008 after having published four articles together.

Introduction. Presentation to the IRS’ offices in Boston, Massachusetts on using Benford’s Law to detect income tax evasion.

Steven Miller in action. Presentation to the IRS’ offices in Boston, Massachusetts on using Benford’s Law to detect income tax evasion.

Mark Nigrini in action. Presentation to the IRS’ offices in Boston, Massachusetts on using Benford’s Law to detect income tax evasion.

Question time. Presentation to the IRS’ offices in Boston, Massachusetts on using Benford’s Law to detect income tax evasion.

Photo time. Presentation to the IRS’ offices in Boston, Massachusetts on using Benford’s Law to detect income tax evasion.

Final photo. Presentation to the IRS’ offices in Boston, Massachusetts on using Benford’s Law to detect income tax evasion.

Benford's Law (2012) data files

The files below are in a Dropbox folder and are numbered 1 to 26. The descriptions are shown below:

The town and city data set (19,509 records) that is used is several places in the book.
The corporate payments data (Excel format) that is used in Chapters 2 to 6.
The corporate payments data (Access format) that is used in Chapters 2 to 6.
The lake data (Excel format) that is used in Chapters 2 and 12.
The lake data (Access format) that is used in Chapters 2 and 12.
The Excel file with Figure 5.15.
The Excel file with Figure 5.16 and the journal entry data.
The Excel file with Figure 7.8 and the synthetic Benford data.
The Excel file with Figure 8.17 and 8.18.
The Excel file with the 1978 taxable incomes data (used for Figure 8.17 and 8.18).
The Excel file with Figures 9.5 and 9.6.
The Excel file with Figure 10.1 and 10.2.
The Excel file with Figure 10.4 and 10.4 and the underlying Sino-Forest data.
The 2000 and 2010 census data used for Figures 10.16, 10.17, and 10.18.
The General Motors payments data used in Figure 11.6 in a pdf format.
The Excel file with Figure 11.5 and the underlying data.
The Excel file with the Chrysler payments data used in Figure 11.8 and 11.9.
The Excel file with Figure 11.6 and the underlying General Motors data.
The Excel file with Figure 11.8, figure 11.9, Figure 11.10, and the underlying Chrysler data.
The Excel file with Figure 11.13 and the Madoff returns data.
The Excel file with Figure 11.16 and the Apple returns data.
The Excel file with Figure 12.1 in an Excel format and the underlying streamflow data.
The Excel file with Figure 13.1 (payroll amounts).
The Excel file with Figure 13.2 (payroll amounts).
The Excel file with Figure 13.11 and the underlying Lehman gifts data.
The Access file with the Lehman gifts data in an Access database.

The 500 Fibonacci numbers shown in Figure 3.1 and used for Figure 3.2 can be found here.

benford_ge1 — Official record of Frank Benford's 1938 paper at General Electric.

Benford_Biography — Official biography of Frank Benford at General Electric

benford_ge3 — Extract from Frank Benford's record book, August 18, 1928.

benford_ge4 — First page of the press release announcing the retirement of Frank Benford.

Selected Benford's Law publications

The first chapter of Steven Miller’s book titled Benford’s Law: Theory and Applications published by Princeton Press. The introduction is well-written and interesting, and should be readable by many people depending on how much you remember from your college mathematics classes.

This review paper written by Ralph Raimi a mathematician at the University of Rochester, and published in American Mathematical Monthly in 1976 is an excellent review of the state-of-the-art in 1976.

The Benford Online Bibliography is an open-access non-commercial database of articles, books and other resources related to Benford’s Law, including theoretical, applied, and human-interest aspects of this rapidly evolving field.

Werner Hurlimann’s Benford’s Law bibliography dated July 6, 2006 shows a good snapshot of the state-of-the-art at that time.

An early Benford’s Law article of mine titled “I’ve Got Your Number” published in the Journal of Accountancy in May, 1999. For a pdf version of the article click here.

A Benford’s Law article of mine coauthored with Steven Miller titled “Benford’s Law Applied to Hydrology Data – Results and Relevance to Other Geophysical Data” published in Mathematical Geology in 2007. For a pdf copy of the article click here (click on the PDF Web.Williams.Edu button).

A short report written by Steven Miller and Alex Kossovsky on a Benford’s Law analysis of the 2020 Presidential Election data.