A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

A comprehensive account of economic size distributions around theworld and throughout the yearsIn the course of the past 100 years, economists and appliedstatisticians have developed a remarkably diverse variety of incomedistribution models, yet no single resource convincingly accountsfor all of these models, analyzing their strengths and weaknessessimilarities and differences. Statistical Size Distributions inEconomics and Actuarial Sciences is the first collection tosystematically investigate a wide variety of parametric models thatdeal with income, wealth, and related notions.Christian Kleiber and Samuel Kotz survey, compliment, compareand unify all of the disparate models of income distributionhighlighting at times a lack of coordination between them that canresult in unnecessary duplication. Considering models from eightlanguages and all continents, the authors discuss the social andeconomic implications of each as well as distributions of size ofloss in actuarial applications. Specific models coveredinclude:* Pareto distributions* Lognormal distributions* Gamma-type size distributions* Beta-type size distributions* Miscellaneous size distributionsThree appendices provide brief biographies of some of theleading players along with the basic properties of each of thedistributions. Actuaries, economists, market researchers, socialscientists, and physicists interested in econophysics will findStatistical Size Distributions in Economics and Actuarial Sciencesto be a truly one-of-a-kind addition to the professionalliterature.

Preface.Acknowledgments.1. Introduction.1.1 Our Aims.1.2 Types of Economic Size Distributions.1.3 A Brief Historical Sketch of the Models for StudyingEconomic Size Distributions.1.4 Stochastic Process Models for Size Distributions.2. General Principles.2.1 Some Concepts from Economics.2.2 Hazard Rates, Mean Excess Functions, and Tailweight.2.3 Systems of Distributions.2.4 Generating Systems of Income Distributions.3. Pareto Distributions.3.1 Definitions.3.2 History and Genesis.3.3 Moments and Other Basic Properties.3.4 Characterizations.3.5 Lorenz Curve and Inequality Measures.3.6 Estimation.3.7 Empirical Results.3.8 Stoppa Distributions.3.9 Conic Distribution.3.10 A "log-adjusted" Pareto Distribution.3.11 Stable Distributions.3.12 Further Pareto-type Distributions.4. Lognormal Distribution.4.1 Definition.4.2 History and Genesis.4.3 Moments and Other Basic Properties.4.4 Characterizations.4.5 Lorenz Curve and Inequality Measures.4.6 Estimation.4.7 Three-and four-parameter Lognormal Distributions.4.8 Multivariate Lognormal Distribution.4.9 Empirical Results.4.10 Generalized Lognormal Distribution.4.11 An Asymmetric Log-Laplace Distribution.4.12 Related Distributions.5. Gamma-type Size Distributions.5.1 Generalized Gamma Distribution.5.2 Gamma Distribution.5.3 Log-gamma Distribution.5.4 Inverse Gamma (Vinci) Distribution.5.5 Weibull Distribution.5.6 Log-Gompertz Distribution.6. Beta-type Size Distributions.6.1 (Generalized) Beta Distribution of the Second Kind.6.2 Singh-Maddala Distribution.6.3 Dagum Distribution.6.4 Fisk (log-logistic) and Lomax Distributions.6.5 (Generalized) Beta Distribution of the First Kind.7. Miscellaneous Size Distributions.7.1 Benini Distribution.7.2 Davis Distribution.7.3 Champernowne Distribution.7.4 Benktander Distributions.Appendix A. Biographies.A.1 Vilfredo Federico Domaso Pareto, Marchese di Parigi.A.2 Rodolfo Benini.A.3 Max Otto Lorenz.A.4 Corrado Gini.A.5 Luigi Amoroso.A.6 Raffaele D'Addario.A.7 Robert Pierre Louis Gibrat.A.8 David Gawen Champernowne.Appendix B. Data on Size Distributions.Appendix C. Size Distributions.List of Symbols.References.Author Index.Subject Index.