Pareto Distributions Second Edition by Barry C Arnold ISBN 0367738473 9780367738471

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Product details: 

ISBN 10: 0367738473

ISBN 13: 9780367738471

Author: Barry C. Arnold

Table of contents: 

1 Historical sketch with emphasis on income modeling
1.1 Introduction
1.2 The First Steps
1.3 The Modern Era
2 Models for income distributions
2.1 What Is a Model?
2.2 The Law of Proportional Effect (Gibrat)
2.3 A Markov Chain Model (Champernowne)
2.4 The Coin Shower (Ericson)
2.5 An Open Population Model (Rutherford)
2.6 The Yule Distribution (Simon)
2.7 Income Determined by Inherited Wealth (Wold-Whittle)
2.8 The Pyramid (Lydall)
2.9 Competitive Bidding for Employment (Arnold and Laguna)
2.10 Other Models
2.11 Parametric Families for Fitting Income Distributions
3 Pareto and related heavy-tailed distributions
3.1 Introduction
3.2 The Generalized Pareto Distributions
3.3 Distributional Properties
3.3.1 Modes
3.3.2 Moments
3.3.3 Transforms
3.3.4 Standard Pareto Distribution
3.3.5 Infinite Divisibility
3.3.6 Reliability,
3.3.7 Convolutions
3.3.8 Products of Pareto Variables
3.3.9 Mixtures, Random Sums and Random Extrema
3.4 Order Statistics
3.4.1 Ratios of Order Statistics
3.4.2 Moments
3.4.3 Moments in the Presence of Truncation
3.5 Record Values
3.6 Generalized Order Statistics
3.7 Residual Life
3.8 Asymptotic Results
3.8.1 Order Statistics
3.8.2 Convolutions
3.8.3 Record Values
3.8.4 Generalized Order Statistics
3.8.5 Residual Life
3.8.6 Geometric Minimization and Maximization
3.8.7 Record Values Once More
3.9 Characterizations
3.9.1 Mean Residual Life
3.9.2 Truncation Equivalent to Rescaling
3.9.3 Inequality Measures
3.9.4 Under-reported Income
3.9.5 Functions of Order Statistics
3.9.6 Record Values
3.9.6 Record Values
3.9.8 Entropy Maximization
3.9.9 Pareto (III) Characterizations
3.9.10 Two More Characterizations
3.10 Related Distributions
3.11 The Discrete Pareto (Zipf) Distribution
3.11.1 Zeta Distribution
3.11.2 Zipf Distributions
3.11.3 Simon Distributions
3.11.4 Characterizations
3.12 Remarks
4 Measures of inequality
4.1 Apologia for Prolixity
4.2 Common Measures of Inequality of Distributions
4.2.1 The Lorenz Curve
4.2.2 Inequality Measures Derived from the Lorenz Curve
4.2.3 The Effect of Grouping
4.2.4 Multivariate Lorenz Curves
4.2.5 Moment Distributions
4.2.6 Related Reliability Concepts
4.2.7 Relations Between Inequality Measures
4.2.8 Inequality Measures for Specific Distributions
4.2.9 Families of Lorenz Curves
4.2.10 Some Alternative Inequality Curves
4.3 Inequality Statistics
4.3.1 Graphical Techniques
4.3.2 Analytic Measures of Inequality
4.3.3 The Sample Gini Index
4.3.4 Sample Lorenz Curve
4.3.5 Further Sample Measures of Inequality
4.3.6 Relations Between Sample Inequality Measures
4.4 Inequality Principles and Utility
4.4.1 Inequality Principles
4.4.2 Transfers, Majorization and the Lorenz Order
Remarks.
4.4.3 How Transformations Affect Inequality
4.4.4 Weighting and Mixing
4.4.5 Lorenz Order within Parametric Families
4.4.6 The Lorenz Order and Order Statistics
4.4.7 Related Orderings
4.4.8 Multivariate Extensions of the Lorenz Order
4.5 Optimal Income Distributions
5 Inference for Pareto distributions
5.1 Introduction
5.2 Parameter Estimation
5.2.1 Maximum Likelihood
5.2.2 Best Unbiased and Related Estimates
5.2.3 Moment and Quantile Estimates
5.2.4 A Graphical Technique
5.2.5 Bayes Estimates
5.2.6 Bayes Estimates Based on Other Data Configurations
5.2.7 Bayes Prediction
5.2.8 Empirical Bayes Estimation
5.2.9 Miscellaneous Bayesian Contributions
5.2.10 Maximum Likelihood for Generalized Pareto Distributions
5.2.11 Estimates Using the Method of Moments and Estimating Equations for Generalized Pareto Distributions
5.2.12 Order Statistic Estimates for Generalized Pareto Distributions
5.2.13 Bayes Estimates for Generalized Pareto Distributions
5.3 Interval Estimates
5.4 Parametric Hypotheses
5.5 Tests to Aid in Model Selection
5.6 Specialized Techniques for Various Data Configurations
5.7 Grouped Data
5.8 Inference for Related Distributions
5.8.1 Zeta Distribution
5.8.2 Simon Distributions
5.8.3 Waring Distribution
5.8.4 Under-reported Income Distributions
5.8.5 Inference for Flexible Extensions of Pareto Models
5.8.6 Back to Pareto
6 Multivariate Pareto distributions
6.0 Introduction
6.1 A Hierarchy of Multivariate Pareto Models
6.1.1 Mardia’s First Multivariate Pareto Model
6.1.2 A Hierarchy of Generalizations
6.1.3 Distributional Properties of the Generalized Multivariate Pareto Models
6.1.4 Some Characterizations of Multivariate Pareto Models
6.2 Alternative Multivariate Pareto Distributions
6.2.1 Mixtures of Weibull Variables
6.2.2 Transformed Exponential Variables
6.2.3 Trivariate Reduction
6.2.4 Geometric Minimization and Maximization
6.2.5 Building Multivariate Pareto Models Using Independent Gamma Distributed Components
6.2.6 Other Bivariate and Multivariate Pareto Models
6.2.7 General Classes of Bivariate Pareto Distributions
6.2.8 A Flexible Multivariate Pareto Model
6.2.9 Matrix-variate Pareto Distributions
6.3 Related Multivariate Models
6.3.1 Conditionally Specified Models
6.3.2 Multivariate Hidden Truncation Models
6.3.3 Beta Extensions
6.3.4 Kumaraswamy Extensions
6.3.5 Multivariate Semi-Pareto Distributions
6.4 Pareto and Semi-Pareto Processes
6.5 Inference for Multivariate Pareto Distributions
6.5.1 Estimation for Mardia’s Multivariate Pareto Families
6.5.2 Estimation for More General Multivariate Pareto Families
6.5.3 A Confidence Interval Based on a Multivariate Pareto Sample
6.5.4 Remarks

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Barry C Arnold,Distributions,Pareto