Statistical Size Distributions in Economics and Actuarial Sciences

Acknowledgments.

1. Introduction.

1.1 Our Aims.

1.2 Types of Economic Size Distributions.

1.3 A Brief Historical Sketch of the Models for Studying Economic 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.