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.
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