Pareto Distributions: 2nd Edition (Hardback) book cover

Pareto Distributions

2nd Edition

By Barry C. Arnold

Chapman and Hall/CRC

456 pages | 6 B/W Illus.

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Hardback: 9781466584846
pub: 2015-03-10
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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


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


The Generalized Pareto Distributions

Distributional Properties

Order Statistics

Record Values

Generalized Order Statistics

Residual Life

Asymptotic Results


Related Distributions

The Discrete Pareto (Zipf) Distribution


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


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


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


Subject Index

Author Index

About the Author

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.

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General