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                                    Benford's Law

Benford's Law by Mark Nigrini is available from Amazon and from Wiley.

My thanks go to Andrew Fitzgibbon in the U.K. for posting an excellent review of Benford's Law on his website.  Welcome to the "Fans of Benford" club.

Click here for an outline of my conference presentation Benford's Law: The Facts, the Fun, and the Future.

Click here for my Facebook page Benford's Law by Mark Nigrini.

Data sets and templates related to Benford's Law:

Chapter 1 to 7: The census data set that is used for several applications.  In the book I might use all the records (19,509 records) or I might only use the numbers that are 10 and higher (19,482 records).  Updated data has recently been released by the U.S. Census Bureau.  The new data should also conform nearly perfectly to Benford's Law.

Chapters (all): The Nigrini Cycle template (Excel 2007 and compatible with Excel 2010).  The graphs and the data profile will only be correct if the instructions for formula updating in cell H2 are followed.

Chapter 2 to 6: The corporate payments data shows several anomalies and is used to demonstrate some of the Nigrini cycle tests.

Chapter 2: Lake data and the Nigrini Cycle.

Chapter 3: First 500 Fibonacci numbers used in Figures 3.1 and 3.2.
Chapter 5: The Minitab file with simulated data with the calculated differences used in Figure 5.11.
Chapter 5: Journal entry data used for Figure 5.15 and Figure 5.16.  The source data is in the Figure 5.16 file.
Chapter 7: The synthetic Benford Set in Figure 7.8.
Chapter 8: Excel file for Figure 8.17 and Figure 8.18.  Data file with 1978 taxable incomes.
Chapter 9: Excel file for Figure 9.5 and Figure 9.6.  
Chapter 10: Excel file for Figure 10.1 and Figure 10.2.  Excel file with data for Figure 10.3 and 10.4.  Census data used for Figures 10.16 to 10.18.
Chapter 11: Figure 11.5 Excel graph with GM trade payables data.  Figure 11.6 Excel graph with GM payments data.

The Chrysler data for Figure 11.8 can be downloaded from the trustee's website.  Click on "Old Carco LLC (f/k/a/ Chrysler LLC)-09-50002".

Figure 11.13 Excel file with Madoff returns data.  Figure 11.16 Excel file with Apple returns data.

Chapter 12: Figure 12.1 Excel file with stream flow data (34 MB).
Chapter 13: Figure 13.1 Excel file with payroll data.  Figure 13.2 Excel file with payroll data.

Lehman charitable gifts: Trustee website (click on the Public>Statements of Financial Affairs in the Categories on the left and then select Lehman Brothers Holdings Inc. as the entity.  The gifts start on page 268 of 341).  If you are having difficulty finding their Statement of Financial Affairs please click here for an extract from that document listing the gifts and charitable contributions.

End of Benford's Law data sets and files.  Please send me an e-mail if there is any file that you would like to see added to the collection.
My Benford's Law Facebook page is up and running, and in need of some more "Likes."
Click here for the excellent online Benford's Law bibliography, with about 800 books, articles, and journal papers.  The website was created by Drs. Arno Berger and Ted Hill, two outstanding scholars. and the authors of "A Basic Theory of Benford's Law.

Click here for a pdf file with an extensive Benford's Law bibliography prepared by Dr. Werner Hürlimann in Switzerland.


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Frank Albert. Benford, Jr. 1912

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Frank A. Benford, Jr.1883-1948

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Lunch with Harry Benford

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Son of Frank Benford, 12/1993

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Home of Frank A. Benford

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Rugby Road, Schenectady, NY

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Photos taken April 22, 1994

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A first digit 1

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Pieter Allaart, Mark Nigrini, Ted Hill, Vrije Universiteit, 1994

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Prof. Ralph A. Raimi, joint seminar, Niagara Falls, 11/1996

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Prof. Ralph A. Raimi, joint seminar, Niagara Falls, 11/1996

Dartmouth College, December, 2000.  Benford's Law presentation titled "Benford's Law, Its a secret law of numbers."  RealVideo and slides.  You need to click on my presentation title to start the video.  Title should be viewable when you go to the page.


Notes on Frank Benford

Official record at GE of Frank Benford's paper
A later "numbers" paper by Frank Benford
An extract from Frank Benford's record book (his own handwriting)
This is the first page of the official General Electric press release dated 1948 announcing the retirement of Frank Benford.
This is a scan of the first page of the original official copy of Benford's 1938 paper as archived at the GE Research Laboratory.  Note "Reprint" in the bottom left corner.
This is a scan of the official biography of Frank Benford in the GE archives.  The scanned image has been cut and pasted into a Word document.

Please do not copy these images to another website.  It took some effort on my part to find and collect these documents.

Can Benford's Law be used in Forensic Accounting?

This was my first published Benford's Law article.  It was a two-page article published in The Balance Sheet, the journal of the Investigative and Forensic Accounting Interest Group of the Canadian Institute of Chartered Accountants.  I made quite a bold prediction about analysis of digital frequencies and the audit of tabulated data.  The article was published in June, 1993 and was written in early 1993.

Page 1 - top part

Page 1 - bottom part (shows the Benford proportions for first, second, and third digits)

Page 2 - top part

Page 2 - bottom part (contains my prediction for analysis of digit frequencies in auditing)

May, 2004. has finally come home!  This name was registered by a cybersquatter in 1999 very soon after my Benford's Law paper was published in The Journal of Accountancy.  For a year or two lived in New Jersey and it then moved to a company with a registered office on Sahara Avenue in Las Vegas.  I visited the office in October, 2002 to ask about buying  To see the old office in Las Vegas, click here.

CBS detective drama Numbers (spelled Numb3rs).

The episode on February 3, 2006 spoke about Benford's Law.  I was flying from Cleveland to Montreal when the show was aired and as of now I have still not yet seen the episode.  Comments sent to me by e-mail are welcome.

Nigrini Benford's Law presentation on YouTube:

My Benford's Law presentation (in four parts) from April 1, 2008 can be seen here:

Copyright © 2002-2012 by Mark J. Nigrini.  All rights reserved.

Except as permitted under the United States Copyright Act of 1976, no part of this web page may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher.  Requests for such permissions should be addressed to Mark J. Nigrini.



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Mark J. Nigrini Ph.D.

55 Heath Court, Pennington, New Jersey, 08534

Tel: (609) 303-0533  E-mail: mark_nigrini at msn dot com