In my opinion it is not that Benford's law is over-rated, just
that it is mechanically overworked with data in accounting. It is a
very useful technique in accounting forensics and is in fact used
extensively in practice.
It is our job as academics to provide a theoretical basis for its use rather than use it simply in a mechanical fashion. That is what people in other domains do. For example, parametric extensions of Benford's law have been shown to better approximate the behaviour of certain integer sequences (for example, prime numbers follow Benford's law asymptotically, but for smaller primes less than 10,000 they do not follow Benford's law at all but follow Pareto Benford law). Such extensions have been found to be useful in some domains. I can cite the following example among thousands that exist.
Dorp, J.R. van and S. Kotz (2002). The standard two-sided power distribution and its
properties : with applications in financial engineering. The American Statistician
56(2), 90-99.
Simon Newcomb not being remembered is probably his bad karma coming back to haunt him. He was a good friend of the Peirce family and in fact was a frequent guest at their house. However, he did not seem to like the Benjamin Peirce's son, one of my heroes Charles Santiago Sanders Peirce whom Bertrand Russell called "one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever". The Santiago in his name was added to indicate CS Peirce's gratitude to his biggest supporter at Harvard, William James. Santiago is the Spanish for St. James.
Newcomb haunted CS Peirce most of his adult life and ensured that he did not succeed. When Peirce was up for tenure at Johns Hopkins and the president was about to sign his tenure, Newcomb informed him that Peirce had lived and traveled with a woman who was not his wife (Peirce then was separated from his first wife but they were not divorced then; later they divorced and he married the lady). He was denied tenure. Later, towards the end of his life he had applied for a grant to publish his work to Carnegie Foundation, but was rejected, thanks to Newcomb who served on their board. Tragically, he spent much of his life in abject poverty, supported by his friends such as William James. John Dewey was a student of Peirce at Johns Hopkins.
Today, CS Peirce is revered around the world as one of the most profound philosophers, but Nwecomb is largely forgotten. Provides some evidence that bad deeds do come back to haunt.
It is our job as academics to provide a theoretical basis for its use rather than use it simply in a mechanical fashion. That is what people in other domains do. For example, parametric extensions of Benford's law have been shown to better approximate the behaviour of certain integer sequences (for example, prime numbers follow Benford's law asymptotically, but for smaller primes less than 10,000 they do not follow Benford's law at all but follow Pareto Benford law). Such extensions have been found to be useful in some domains. I can cite the following example among thousands that exist.
Dorp, J.R. van and S. Kotz (2002). The standard two-sided power distribution and its
properties : with applications in financial engineering. The American Statistician
56(2), 90-99.
Statisticians
have looked at the problem from two different perspectives: 1. what are
the common distributions that follow Benford's law (suggested by
Theodore Hill in a paper in 1995), and 2. Find a process that generates
Benfor'd compliant data. We in accounting need to ask the question what
is the process that generates the data and then see under what
conditions the data approximates Benford. My point is that most Benford
studies in accounting I have seen (including the SSRN paper you sent the
links to) have really no accounting content; they are merely mechanical
application of Benford's law to accounting data.
And, most
importantly, the discovery of the so-called Benford's law was not by
Benford, but by the Canadian-American astronomer Simon Newcomb who, in
1881 in an article in the journal American Journal of Mathematics,
expressed it as "The law of probability of the occurrence of numbers is
such that all mantissae of their logarithms are equally likely".
Benford was only two years old when Newcomb wrote that paper. History
has been rather cruel to Newcomb. (I am attaching to this message one of
the best presentations of "Benford's" law I have seen).Simon Newcomb not being remembered is probably his bad karma coming back to haunt him. He was a good friend of the Peirce family and in fact was a frequent guest at their house. However, he did not seem to like the Benjamin Peirce's son, one of my heroes Charles Santiago Sanders Peirce whom Bertrand Russell called "one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever". The Santiago in his name was added to indicate CS Peirce's gratitude to his biggest supporter at Harvard, William James. Santiago is the Spanish for St. James.
Newcomb haunted CS Peirce most of his adult life and ensured that he did not succeed. When Peirce was up for tenure at Johns Hopkins and the president was about to sign his tenure, Newcomb informed him that Peirce had lived and traveled with a woman who was not his wife (Peirce then was separated from his first wife but they were not divorced then; later they divorced and he married the lady). He was denied tenure. Later, towards the end of his life he had applied for a grant to publish his work to Carnegie Foundation, but was rejected, thanks to Newcomb who served on their board. Tragically, he spent much of his life in abject poverty, supported by his friends such as William James. John Dewey was a student of Peirce at Johns Hopkins.
Today, CS Peirce is revered around the world as one of the most profound philosophers, but Nwecomb is largely forgotten. Provides some evidence that bad deeds do come back to haunt.
