DOS NOVEDADES SOBRE LA LEY DE BENFORD

1) AN INTRODUCTION TO BENFORD’S LAW

Arno Berger (University of Alberta. Edmonton, Alberta. Canada) y  Theodore P. Hill (California Polytechnic State University, San Luis Obispo, California. USA)

Princeton, New Jersey. USA. PRINCETON University Press. ISBN: 9780691163062. 256 págs. Mayo de 2015. Encuadernado

PVP 79,00 EUR (4% IVA incluido)

Este libro ofrece el primer tratamiento integral de la ley de Benford, la sorprendente distribución logarítmica de dígitos significativos descubiertos a finales del siglo XIX. Estableciendo los principios matemáticos y estadísticos que sustentan este fenómeno intrigante, el texto combina los resultados hasta a la fecha teóricos con una visión general de la curiosa historia de la ley,  en rápido desarrollo de la parte principal de la evidencia empírica, y una amplia gama de aplicaciones.

Diagramas seleccionados cuidadosamente, tablas y cerca de 150 ejemplos aclaran los conceptos principales. El texto incluye muchos problemas abiertos, además de decenas de nuevos teoremas básicos y todas las referencias importantes.

 

Extracto del índice:

Preface

-1 Introduction

1.1 History

1.2 Empirical evidence

1.3 Early explanations

1.4 Mathematical framework

-2 Significant Digits and the Significand

2.1 Significant digits

2.2 The significand

2.3 The significand s-algebra

-3 The Benford Property

3.1 Benford sequences

3.2 Benford functions

3.3 Benford distributions and random variables

-4 The Uniform Distribution and Benford’s Law

4.1 Uniform distribution characterization of Benford’s law

4.2 Uniform distribution of sequences and functions

4.3 Uniform distribution of random variables

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

5.1 The scale-invariance property

5.2 The base-invariance property

5.3 The sum-invariance property

-6 Real-valued Deterministic Processes

6.1 Iteration of functions

6.2 Sequences with polynomial growth

6.3 Sequences with exponential growth

6.4 Sequences with super-exponential growth

6.5 An application to Newton’s method

6.6 Time-varying systems

6.7 Chaotic systems: Two examples

6.8 Differential equations

-7 Multi-dimensional Linear Processes

7.1 Linear processes, observables, and difference equations

7.2 Nonnegative matrices

7.3 General matrices

7.4 An application to Markov chains

7.5 Linear difference equations

7.6 Linear differential equations

-8 Real-valued Random Processes

8.1 Convergence of random variables to Benford’s law

8.2 Powers, products, and sums of random variables

8.3 Mixtures of distributions

8.4 Random maps

-9 Finitely Additive Probability and Benford’s Law

9.1 Finitely additive probabilities

9.2 Finitely additive Benford probabilities

-10 Applications of Benford’s Law

10.1 Fraud detection

10.2 Detection of natural phenomena

10.3 Diagnostics and design

10.4 Computations and Computer Science

10.5 Pedagogical tool

List of Symbols

Bibliography

Index

 

2) BENFORD’S LAW

Theory and Applications

Steven J. Miller (Williams College, Williamstown, MA, USA)

Princeton, New Jersey. USA. PRINCETON University Press. ISBN: 9780691147611. 472 págs. Mayo de 2015. Encuadernado

PVP 83,00 EUR (4% IVA incluido)

La ley de Benford establece que los dígitos iniciales de muchos conjuntos de datos no se distribuyen de manera uniforme desde uno al nueve, sino que muestran un sesgo profundo. Este sesgo es evidente en todo, como en las facturas de electricidad, las cifras de población, tasas de mortalidad, y las longitudes de los ríos… etc. Aquí, Steven Miller reúne a muchos de los principales expertos del mundo sobre la ley de Benford para demostrar las muchas técnicas útiles que se derivan de la ley, mostrando lo verdaderamente multidisciplinaria que es, y animando a la colaboración.

Haciendo hincapié en los desafíos y las técnicas comunes a través de las diversas disciplinas, este comprensible libro muestra cómo la ley de Benford puede servir como un punto de encuentro productivo para investigadores y profesionales en diversos campos.

 

Extracto del índice:

-General Resources:

Berger and Hill: Benford Online Bibliography.

Hurlimann: Benford’s Law from 1881 to 2006: A Bibliography

-Part I: General Theory I: Basis of Benford’s Law:

Chapter 1: A Quick Introduction to Benford’s Law (Miller)

Chapter 2: A Short Introduction to the Mathematical Theory of Benford’s Law (Berger and Hill)

Chapter 3: Fourier Analysis and Benford’s Law (Miller)

-Part II: General Theory II: Distributions and Rates of Convergence:

Chapter 4: Benford’s Law Geometry (Leemis)

Chapter 5: Explicit Error Bounds via Total Variation (Dümbgen and Christoph Leuenberger)

Chapter 6: Lévy Processes and Benford’s Law (Schürger)

-Part III: Applications I: Accounting and Vote Fraud:

Chapter 7: Benford’s Law as a Bridge between Statistics and Accounting (Cleary and Thibodeau)

Chapter 8: Detecting Fraud and Errors Using Benford’s Law (Nigrini)

Chapter 9: Can Vote Counts’ Digits and Benford’s Law Diagnose Elections? (Mebane)

Chapter 10: Complementing Benford’s Law for small N: a local bootstrap (Roukema)

-Part IV: Applications II: Economics:

Chapter 11: Measuring the Quality of European Statistics (Rauch, Göttsche, Brähler and Engel)

Chapter 12: Benford’s Law and Fraud in Economic Research (Tödter)

Chapter 13: Testing for Strategic Manipulation of Economic and Financial Data (Moul and Nye)

-Part V: Applications III: Psychology and the Sciences:

Chapter 14: Psychology and Benford’s Law (Burns and Krygier)

Chapter 15: Managing Risk in Numbers Games (Chou, Kong, Teo and Zheng)

Chapter 16: Benford’s Law in the Natural Sciences (Hoyle)

Chapter 17: Generalizing Benford’s Law (Lee, Cho and Judge)

-Part VI: Applications IV: Images:

Chapter 18: PV Modeling of Medical Imaging Systems (Chiverton and Wells)

Chapter 19: Application of Benford’s Law to Images (Pérez-González, Quach, Abdallah, Heileman and Miller)

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