- 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
Explicit Error Bounds via Total Variation
Explicit Error Bounds via Total Variation
- Chapter:
- (p.119) Chapter Five Explicit Error Bounds via Total Variation
- Source:
- Benford's Law
- Author(s):
Lutz Dümbgen
Christoph Leuenberger
- Publisher:
- Princeton University Press
This chapter concerns the obtaining of explicit error estimates for convergence to Benford's law, with an analysis done through the total variation of the densities. This method yields reasonable estimates for Benford's law in many cases, and is often simpler to calculate and more elementary than Fourier methods. Here, the chapter provides the distribution of the remainder U in the case of Y having a Lebesgue density f, defines the measures of non-uniformity of this distribution, and collects some basic facts about the total variation of functions. The main results, examples, and proofs are then presented in the final three sections of this chapter.
Keywords: explicit error estimates, total variation, explicit error bounds, non-uniformity, densities, functions
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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
