| Acknowledgments | 7 |
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| Contents | 8 |
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| List of Figures | 11 |
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| List of Tables | 13 |
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| Introduction | 15 |
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| Chapter 1: Measuring the Wellbeing of Groups | 19 |
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| 1.1 Introduction | 19 |
| 1.2 An Outline of What Follows | 21 |
| 1.3 Measuring Wellbeing: The Social Welfare Function | 24 |
| 1.4 Measuring Wellbeing: The Benthamite Tradition | 28 |
| 1.5 The Pigou-Dalton Principle: “Inequality Is a Bad Thing” | 29 |
| 1.6 Polarization | 30 |
| 1.7 Social Exclusion | 31 |
| 1.8 Equality of Opportunity and Social Mobility | 34 |
| 1.9 The Rawlsian Principle and the Focus on Poverty | 36 |
| 1.10 What to Do Now? | 36 |
| References | 37 |
| Chapter 2: Statistical Matters | 40 |
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| 2.1 Introduction | 40 |
| 2.2 Probability Distributions | 41 |
| Multivariate Considerations | 43 |
| Statistical Independence | 45 |
| Independence and Random Samples | 47 |
| Independence and Groups | 47 |
| Measures of Location and Dispersion | 48 |
| Means and Variances and the Expectations Operator | 48 |
| Location Measures | 51 |
| Inequality Measures | 51 |
| Some Unit Free Inequality Measures | 51 |
| 2.3 Parametric and Non-Parametric Distributions | 54 |
| An Example of a Discrete Probability Density Function: The Poisson Distribution | 54 |
| An Example of Continuous Probability Density Function: The Normal Distribution | 56 |
| Multidimensional Considerations | 58 |
| A Note of Caution | 58 |
| The Normal Distribution and Central Limit Theorems | 59 |
| Estimation of Unknown Parameters | 60 |
| 2.4 Kernel Estimation | 60 |
| Non-Parametric Distributions | 60 |
| The Kernel Function | 61 |
| Choosing the “H” and the Kernel | 62 |
| Choosing “H” | 63 |
| Least Squares Cross Validation | 64 |
| Likelihood C
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