By Arno Berger,Theodore P. Hill
This ebook presents the 1st finished therapy of Benford's legislation, the astounding logarithmic distribution of vital digits came upon within the overdue 19th century. developing the mathematical and statistical rules that underpin this fascinating phenomenon, the textual content combines updated theoretical effects with overviews of the law’s colourful historical past, quickly transforming into physique of empirical proof, and wide selection of applications.
An advent to Benford’s Law starts off with easy evidence approximately major digits, Benford services, sequences, and random variables, together with instruments from the idea of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the legislations, the publication develops the significant-digit houses of either deterministic and stochastic approaches, similar to iterations of capabilities, powers of matrices, differential equations, and items, powers, and combos of random variables. concluding chapters survey the finitely additive conception and the flourishing purposes of Benford’s law.
Carefully chosen diagrams, tables, and shut to one hundred fifty examples light up the most strategies all through. The textual content comprises many open difficulties, as well as dozens of latest simple theorems and the entire major references. A distinguishing characteristic is the emphasis at the outstanding ubiquity and robustness of the significant-digit legislations. this article can function either a major reference and a foundation for seminars and courses.
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Extra resources for An Introduction to Benford's Law
An Introduction to Benford's Law by Arno Berger,Theodore P. Hill