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Small is beautiful!

The mathematicians believe it -- the Normal Distribution -- to be a physical fact while the scientists believe it to be a mathematical law -- Poincare, 1854-1912

World Scientific


IMAGE: Benford's Law is the theory, general law of relative quantities, and forensic fraud detection applications by Alex Ely Kossovsky. view more

Credit: World Scientific Publishing, 2015

Quantitatively, mathematically, and scientifically speaking, Mother Nature is very picky, artistic, and discriminating in her daily work and constructions, and so her unique style of creation typically yields many small quantities but very few big quantities. When this pattern is being carefully measured in a rigorous statistical way it shows an almost exact proportion between occurrences of relative quantities across all types of data! The theoretical work in this book developed from basic premises leads to The General Law of Relative Quantities which expresses this proportion as:

ln (D + d (F - 1) / D + (d-1)(F-1) / ln(F)

As a direct consequence of the general law, and quite contrary to common intuition, [first significant] digits are not created equal, but rather 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, and it allocates digital proportions according to LOG10( 1 + 1/d ).

In his book, Benford's Law: Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications, Dr Alex Kossovsky 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. The key finding that the phenomenon is actually quantitative in nature, implies that 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 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 itself, as it is found in all random data sets, Benford as well as non-Benford types.


The hardcover of the book retails for US$155 / £102 and the paperback at US$65 / £43. More information on the book can be found at:

About World Scientific Publishing Co.

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