Contrary to common intuition that all digits should occur randomly with
equal chances in real data, empirical examinations consistently show
that not all digits are created equal, but rather that low digits such
as {1, 2, 3} occur much more frequently than high digits such as {7, 8,
9} in almost all data types, such as those relating to geology,
chemistry, astronomy, physics, and engineering, as well as in
accounting, financial, econometrics, and demographics data sets. This
intriguing digital phenomenon is known as Benford's Law.This book gives
a comprehensive and in-depth account of all the theoretical aspects,
results, causes and explanations of Benford's Law, with a strong
emphasis on the connection to real-life data and the physical
manifestation of the law. In addition to such a bird's eye view of the
digital phenomenon, the conceptual distinctions between digits, numbers,
and quantities are explored; leading to the key finding that the
phenomenon is actually quantitative in nature; originating from the fact
that in extreme generality, nature creates many small quantities but
very few big quantities, corroborating the motto 'small is beautiful',
and that therefore all this is applicable just as well to data written
in the ancient Roman, Mayan, Egyptian, and other digit-less
civilizations.Fraudsters are typically not aware of this digital pattern
and tend to invent numbers with approximately equal digital frequencies.
The digital analyst can easily check reported data for compliance with
this digital law, enabling the detection of tax evasion, Ponzi schemes,
and other financial scams. The forensic fraud detection section in this
book is written in a very concise and reader-friendly style; gathering
all known methods and standards in the accounting and auditing industry;
summarizing and fusing them into a singular coherent whole; and can be
understood without deep knowledge in statistical theory or advanced
mathematics. In addition, a digital algorithm is presented, enabling the
auditor to detect fraud even when the sophisticated cheater is aware of
the law and invents numbers accordingly. The algorithm employs a subtle
inner digital pattern within the Benford's pattern itself. This newly
discovered pattern is deemed to be nearly universal, being even more
prevalent than the Benford phenomenon, as it is found in all random data
sets, Benford as well as non-Benford types.
