- Title Pages
- Dedication
- Foreword
- Preface
- Notation
-
Chapter One A Quick Introduction to Benfordʼs Law -
Chapter Two A Short Introduction to the Mathematical Theory of Benfordʼs Law -
Chapter Three Fourier Analysis and Benfordʼs Law -
Chapter Four Benfordʼs Law Geometry -
Chapter Five Explicit Error Bounds via Total Variation -
Chapter Six Lévy Processes and Benfordʼs Law -
Chapter Seven Benfordʼs Law as a Bridge between Statistics and Accounting -
Chapter Eight Detecting Fraud and Errors Using Benfordʼs Law Mark Nigrini -
Chapter Nine Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections? -
Chapter Ten Complementing Benfordʼs Law for Small N: A Local Bootstrap -
Chapter Eleven Measuring the Quality of European Statistics -
Chapter Twelve Benfordʼs Law and Fraud in Economic Research -
Chapter Thirteen Testing for Strategic Manipulation of Economic and Financial Data -
Chapter Fourteen Psychology and Benfordʼs Law -
Chapter Fifteen Managing Risk in Numbers Games -
Chapter Sixteen Benfordʼs Law in the Natural Sciences -
Chapter Seventeen Generalizing Benfordʼs Law -
Chapter Eighteen PV Modeling of Medical Imaging Systems -
Chapter Nineteen Application of Benfordʼs Law to Images -
Chapter Twenty Exercises - Bibliography
- Index
Fourier Analysis and Benfordʼs Law
Fourier Analysis and Benfordʼs Law
- Chapter:
- (p.68) Chapter Three Fourier Analysis and Benfordʼs Law
- Source:
- Benford's Law
- Author(s):
Steven J. Miller
- Publisher:
- Princeton University Press
This chapter continues the development of the theory of Benford's law. It uses Fourier analysis (in particular, Poisson Summation) to prove many systems either satisfy or almost satisfy the Fundamental Equivalence, and hence either obey Benford's law, or are well approximated by it. Examples range from geometric Brownian motions to random matrix theory to products and chains of random variables to special distributions. The chapter furthermore develops the notion of a Benford-good system. Unfortunately one of the conditions here concerns the cancelation in sums of translated errors related to the cumulative distribution function, and proving the required cancelation often requires techniques specific to the system of interest.
Keywords: Fourier analysis, Poisson Summation, Fundamental Equivalence, Benford-good system, cumulative distribution, uniform distribution
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- Title Pages
- Dedication
- Foreword
- Preface
- Notation
-
Chapter One A Quick Introduction to Benfordʼs Law -
Chapter Two A Short Introduction to the Mathematical Theory of Benfordʼs Law -
Chapter Three Fourier Analysis and Benfordʼs Law -
Chapter Four Benfordʼs Law Geometry -
Chapter Five Explicit Error Bounds via Total Variation -
Chapter Six Lévy Processes and Benfordʼs Law -
Chapter Seven Benfordʼs Law as a Bridge between Statistics and Accounting -
Chapter Eight Detecting Fraud and Errors Using Benfordʼs Law Mark Nigrini -
Chapter Nine Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections? -
Chapter Ten Complementing Benfordʼs Law for Small N: A Local Bootstrap -
Chapter Eleven Measuring the Quality of European Statistics -
Chapter Twelve Benfordʼs Law and Fraud in Economic Research -
Chapter Thirteen Testing for Strategic Manipulation of Economic and Financial Data -
Chapter Fourteen Psychology and Benfordʼs Law -
Chapter Fifteen Managing Risk in Numbers Games -
Chapter Sixteen Benfordʼs Law in the Natural Sciences -
Chapter Seventeen Generalizing Benfordʼs Law -
Chapter Eighteen PV Modeling of Medical Imaging Systems -
Chapter Nineteen Application of Benfordʼs Law to Images -
Chapter Twenty Exercises - Bibliography
- Index
