Synopsis
Numbers are written in our digital language system by conveniently utilizing the ten digits 0 to 9, just as books and text are written in English, French, or German, by conveniently utilizing the 26 letters A to Z. Surprisingly, and against all common sense or intuition, the spread of these ten digits within numbers of random data is not equal and uniform, but rather highly uneven. Benford’s Law predicts that the first digit on the left-most side of numbers is proportioned between all possible 1 to 9 digits as in LOG(1 + 1/digit) in the approximate, so that occurrences of low digits such as 1, 2, 3 in the first place are much more frequent than occurrences of high digits such as 7, 8, 9. Remarkably, Benford’s Law is found to be valid in almost all real-life statistics, such as in data relating to physics, chemistry, astronomy, geology, biology, economics, finance, accounting, engineering, and governmental census information. As such Benford’s Law constitutes a unique common thread running through and uniting data sets relating to all scientific disciplines. This book explores the most recent research results and discoveries in the field of Benford’s Law with a strong emphasis on relevant real-life physical, financial, accounting, scientific, and demographic data, while tying in diverse and seemingly unrelated areas of mathematics such as prime numbers, quantitative partition models, and exponential growth series. The book also explores the resultant quantitative and digital configurations of an arithmetical mix of random variables, such as random addition processes which are known to yield the symmetric Normal Distribution as predicated by the Central Limit Theorem, as well as random multiplication processes which are known to yield the skewed Lognormal Distribution. Thus the involvement of various additive and multiplicative terms within a single expression of a stochastic process or a random variable constitutes a tug of war between these two arithmetical operations. Data relating to physical processes in nature as well as to particular financial and accounting transactions are at times found to be modeled after such arithmetical combinations of additions and multiplications of random variables. In addition, the latest methods in forensic digital analysis in the context of data fraud detection are presented in this book as the main application of the Benford phenomenon, including the most recent innovative techniques utilizing Digital Development Pattern.
Présentation de l'éditeur
Numbers are written in our digital language system by conveniently utilizing the ten digits 0 to 9, just as books and text are written in English, French, or German, by conveniently utilizing the 26 letters A to Z. Surprisingly, and against all common sense or intuition, the spread of these ten digits within numbers of random data is not equal and uniform, but rather highly uneven. Benford’s Law predicts that the first digit on the left-most side of numbers is proportioned between all possible 1 to 9 digits as in LOG(1 + 1/digit) in the approximate, so that occurrences of low digits such as 1, 2, 3 in the first place are much more frequent than occurrences of high digits such as 7, 8, 9. Remarkably, Benford’s Law is found to be valid in almost all real-life statistics, such as in data relating to physics, chemistry, astronomy, geology, biology, economics, finance, accounting, engineering, and governmental census information. As such Benford’s Law constitutes a unique common thread running through and uniting data sets relating to all scientific disciplines. This book explores the most recent research results and discoveries in the field of Benford’s Law with a strong emphasis on relevant real-life physical, financial, accounting, scientific, and demographic data, while tying in diverse and seemingly unrelated areas of mathematics such as prime numbers, quantitative partition models, and exponential growth series. The book also explores the resultant quantitative and digital configurations of an arithmetical mix of random variables, such as random addition processes which are known to yield the symmetric Uniform Distribution as predicated by the Central Limit Theorem, as well as random multiplication processes which are known to yield the skewed Lognormal Distribution. Thus the involvement of various additive and multiplicative terms within a single expression of a stochastic process or a random variable constitutes a tug of war between these two arithmetical operations. Data relating to physical processes in nature as well as to particular financial and accounting transactions are at times found to be modeled after such arithmetical combinations of additions and multiplications of random variables. In addition, the latest methods in forensic digital analysis in the context of data fraud detection are presented in this book as the main application of the Benford phenomenon, including the most recent innovative techniques utilizing Digital Development Pattern.
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