A01=Arno Berger
A01=Theodore P. Hill
Absolute continuity
Age Group_Uncategorized
Age Group_Uncategorized
Algorithm
Almost surely
Approximation
Approximation error
Author_Arno Berger
Author_Theodore P. Hill
automatic-update
Benford's law
Borel set
Calculation
Category1=Non-Fiction
Category=PBC
Coefficient
Continuous function
Convergence of random variables
COP=United States
Countable set
Data set
Delivery_Delivery within 10-20 working days
Differential equation
Dimension
Discrete time and continuous time
Distribution function
Division by zero
Eigenvalues and eigenvectors
Empirical distribution function
Empty set
eq_isMigrated=2
eq_nobargain
Equation
Ergodic theory
Existential quantification
Explanation
Fibonacci number
Independent and identically distributed random variables
Initial value problem
Integer
Language_English
Law of large numbers
Lebesgue measure
Linear difference equation
Linear map
Logarithm
Logarithmic distribution
Mathematics
Monotonic function
Natural density
Natural number
Newton's method
Nonnegative matrix
Normal distribution
Number theory
Open problem
PA=Available
Parameter
Positive real numbers
Power set
Price_€50 to €100
Prime number
Probability
Probability distribution
Probability measure
Probability space
Probability theory
Proportionality (mathematics)
PS=Active
Random variable
Rate of convergence
Real number
Result
Round-off error
Sampling (statistics)
Sign (mathematics)
Significand
Significant figures
softlaunch
Special case
Statistic
Subset
Summation
Theorem
Theory
Uniform distribution (discrete)
Product details
- ISBN 9780691163062
- Weight: 680g
- Dimensions: 152 x 235mm
- Publication Date: 26 May 2015
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
Secure
checkout
Fast Shipping
Easy returns
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.
Arno Berger is associate professor of mathematics at the University of Alberta. He is the author of Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics. Theodore P. Hill is professor emeritus of mathematics at the Georgia Institute of Technology and research scholar in residence at the California Polytechnic State University.
