Content.- 1. Introduction.- 1.1. Study of welfare aspects in economics.- 1.2. Disparities in regional welfare.- 1.3. Selection of regional welfare elements.- 1.4. Methods.- 1.5. Layout.- 2. Statistical and Related Income Inequality Measures, With No Explicit Specification of a Probability Density- or Welfare-Function.- 2.1. The concept of an inequality measure.- 2.2. Notations.- 2.3. Statistical and other non-welfare-based inequality measures with an unspecified p.d.f..- 2.3.1. Partial statistical indicators of dispersion.- 2.3.2. Functions of simple location parameters and ordinary moments.- 2.3.3. The first absolute moment and related inequality measures.- 2.3.4. The mean difference and related measures.- 2.3.5. Some general divergence measures.- 2.3.6. Some measures related to entropy.- 2.4. A partial evaluation of statistical and related inequality measures.- Appendix 2A. Elementary definitions.- Appendix 2B. Partial statistical indicators of dispersion.- Appendix 2C. Decomposition formulae.- 3. Explicit Probability Density Functions of Income.- 3.1. The usefulness of an explicit probability density function of income.- 3.2. Alternative approaches and selection criteria for defining a set of p.d.f.s.- 3.3. A direct definition of a skew p.d.f. of income.- 3.4. A definition of a skew p.d.f. of income using transformations.- 3.4.1. The lognormal distribution.- 3.4.2. The inverse hyperbolic sine normal distribution.- 3.4.3. The log logistic or sech distribution.- 3.4.4. The Champernowne distribution.- 3.4.5. The log Student p.d.f..- 3.4.6. The Box Cox Champernowne distribution.- 3.4.7. The Beta distribution.- 3.5. A preliminary evaluation of some p.d.f.s.- 3.6. Methods of parameter estimation.- 3.7. Aspects of goodness of fit.- 3.8. Concluding remarks.- Appendix 3A. The Pareto distribution.- 4. Income Inequality Measures and Welfare Functions of Income.- 4.1. The use of a welfare function of income.- 4.2. A partial group welfare function of incomes.- 4.3. An additivlD