By Arno Berger,Theodore P. Hill
This e-book presents the 1st finished remedy of Benford's legislations, the unbelievable logarithmic distribution of vital digits found within the past due 19th century. constructing the mathematical and statistical ideas that underpin this interesting phenomenon, the textual content combines updated theoretical effects with overviews of the law’s colourful heritage, quickly becoming physique of empirical facts, and wide selection of applications.
An advent to Benford’s Law starts off with uncomplicated evidence approximately major digits, Benford features, sequences, and random variables, together with instruments from the speculation of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the legislation, the ebook develops the significant-digit homes of either deterministic and stochastic strategies, akin to iterations of features, powers of matrices, differential equations, and items, powers, and combos of random variables. concluding chapters survey the finitely additive conception and the flourishing functions of Benford’s law.
Carefully chosen diagrams, tables, and shut to one hundred fifty examples remove darkness from the most innovations all through. The textual content comprises many open difficulties, as well as dozens of latest uncomplicated theorems and all of the major references. A distinguishing characteristic is the emphasis at the amazing ubiquity and robustness of the significant-digit legislations. this article can function either a main 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