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2nd Edition

Pareto Distributions




ISBN 9781466584846
Published March 10, 2015 by Chapman and Hall/CRC
456 Pages - 6 B/W Illustrations

 
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Book Description

Since the publication of the first edition over 30 years ago, the literature related to Pareto distributions has flourished to encompass computer-based inference methods. Pareto Distributions, Second Edition provides broad, up-to-date coverage of the Pareto model and its extensions. This edition expands several chapters to accommodate recent results and reflect the increased use of more computer-intensive inference procedures.

New to the Second Edition

  • New material on multivariate inequality
  • Recent ways of handling the problems of inference for Pareto models and their generalizations and extensions
  • New discussions of bivariate and multivariate income and survival models

This book continues to provide researchers with a useful resource for understanding the statistical aspects of Pareto and Pareto-like distributions. It covers income models and properties of Pareto distributions, measures of inequality for studying income distributions, inference procedures for Pareto distributions, and various multivariate Pareto distributions existing in the literature.

Table of Contents

Historical Sketch with Emphasis on Income Modeling
Introduction
The First Steps
The Modern Era

Models for Income Distributions
What Is a Model?
The Law of Proportional Effect (Gibrat)
A Markov Chain Model (Champernowne)
The Coin Shower (Ericson)
An Open Population Model (Rutherford)
The Yule Distribution (Simon)
Income Determined by Inherited Wealth (Wold-Whittle)
The Pyramid (Lydall)
Competitive Bidding for Employment (Arnold and Laguna)
Other Models
Parametric Families for Fitting Income Distributions

Pareto and Related Heavy-Tailed Distributions
Introduction
The Generalized Pareto Distributions
Distributional Properties
Order Statistics
Record Values
Generalized Order Statistics
Residual Life
Asymptotic Results
Characterizations
Related Distributions
The Discrete Pareto (Zipf) Distribution
Remarks

Measures of Inequality
Apologia for Prolixity
Common Measures of Inequality of Distributions
Inequality Statistics
Inequality Principles and Utility
Optimal Income Distributions

Inference for Pareto Distributions
Introduction
Parameter Estimation
Interval Estimates
Parametric Hypotheses
Tests to Aid in Model Selection
Specialized Techniques for Various Data Configurations
Grouped Data
Inference for Related Distributions

Multivariate Pareto Distributions
Introduction
A Hierarchy of Multivariate Pareto Models
Alternative Multivariate Pareto Distributions
Related Multivariate Models
Pareto and Semi-Pareto Processes
Inference for Multivariate Pareto Distributions
Multivariate Discrete Pareto (Zipf) Distributions

Appendix A: Historical Income Data Sources
Appendix B: Two Representative Data Sets
Appendix C: A Quarterly Household Income Data Set

References

Subject Index
Author Index

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Author(s)

Biography

Barry C. Arnold is a distinguished professor in the Department of Statistics at the University of California, Riverside. Dr. Arnold is a fellow of the American Statistical Association and the Institute of Mathematical Statistics and an elected member of the International Statistical Institute.