Pareto Distributions

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.

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 PropertiesOrder 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

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.