An Introduction to Benford's Law / Theodore P. Hill, Arno Berger.

Format:

Book

Author/Creator:

Berger, Arno, author.

Hill, Theodore P., author.

Language:

English

Subjects (All):

Distribution (Probability theory).

Probability measures.

Physical Description:

1 online resource (257 p.)

Edition:

Course Book

Place of Publication:

Princeton, NJ : Princeton University Press, [2015]

Language Note:

English

Summary:

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 law's colorful history, rapidly growing body of empirical evidence, and wide range of applications.An Introduction to Benford's Law begins 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 Benford's 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.

Contents:

Frontmatter

Contents

Preface

1. Introduction

2. Significant Digits and the Significand

3. The Benford Property

4. The Uniform Distribution and Benford's Law

5. Scale-, Base-, and Sum-Invariance

6. Real-valued Deterministic Processes

7. Multi-dimensional Linear Processes

8. Real-valued Random Processes

9. Finitely Additive Probability and Benford's Law

10. Applications of Benford's Law

List of Symbols

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)

ISBN:

9781400866588

OCLC:

906575018