An Introduction to Benford's Law [Hardcover]

This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the laws colorful history, rapidly growing body of empirical evidence, and wide range of applications.

An Introduction to Benfords Lawbegins with basic facts about significant digits, Benford functions, sequences, and random variables, including tools from the theory of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the law, the book develops the significant-digit properties of both deterministic and stochastic processes, such as iterations of functions, powers of matrices, differential equations, and products, powers, and mixtures of random variables. Two concluding chapters survey the finitely additive theory and the flourishing applications of Benfords law.

Carefully selected diagrams, tables, and close to 150 examples illuminate the main concepts throughout. The text includes many open problems, in addition to dozens of new basic theorems and all the main references. A distinguishing feature is the emphasis on the surprising ubiquity and robustness of the significant-digit law. This text can serve as both a primary reference and a basis for seminars and courses.

Arno Bergeris associate professor of mathematics at the University of Alberta. He is the author ofChaos and Chance: An Introduction to Stochastic Aspects of Dynamics.Theodore P. Hillis professor emeritus of mathematics at the Georgia Institute of Technology and research scholar in residence at the California Polytechnic State University. This is a marvelous and excellent introduction. ---Adhemar Bultheel,European Mathematical Society Bulletin A must-read fl£P