| Contents | 8 |
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| Preface | 17 |
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| List of Contributors | 21 |
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| List of Tables | 26 |
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| List of Figures | 29 |
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| Part I Distribution Theory and Applications | 32 |
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| 1 Enrique Castillos Contributions to Conditional Specification | 33 |
| 1.1 Introduction | 33 |
| 1.2 Conditionals in Given Exponential Families | 34 |
| 1.3 Conditionals in Given Non-Exponential Families | 38 |
| 1.4 Truncated and Weighted Distributions | 39 |
| 1.5 A Digression on Improper Models | 39 |
| 1.6 Characterizations of Classical Models Via Conditional Specifications | 40 |
| 1.7 Back to the Bayesian Scenario | 40 |
| 1.8 Inference for Conditionally Specified Models | 41 |
| 1.9 Incomplete and Imprecise Conditional Specification | 41 |
| 1.10 Future Prospects | 47 |
| References | 47 |
| 2 The Polygonal Distribution | 50 |
| 2.1 Introduction | 50 |
| 2.2 The Triangular Distribution | 51 |
| 2.3 The Polygonal Distribution | 52 |
| 2.4 The Polygonal Distribution as a Mixing Density | 55 |
| 2.5 Discussion | 61 |
| References | 61 |
| 3 Conditionally Specified Models: New Developments and Applications | 63 |
| 3.1 Introduction | 63 |
| 3.2 Bivariate Power Conditionals Distribution | 64 |
| 3.3 Mixture Conditional Models with Applications to Actuarial Statistics | 66 |
| 3.4 Bivariate Income Distributions | 67 |
| 3.5 Flexible Conjugate Prior Families | 67 |
| 3.6 Conditional Hazard Functions | 69 |
| References | 70 |
| 4 Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data | 72 |
| 4.1 Introduction | 72 |
| 4.2 Cross Section versus Panel Data | 74 |
| 4.3 Poisson Distribution | 75 |
| 4.4 Hurdle Models | 76 |
| 4.5 Predictive Distribution | 80 |
| 4.6 Insurance Application | 82 |
| 4.7 Conclusion | 85 |
| References | 85 |
| 5 Distance-Based Association and Multi-Sample Tests for General Multivariate Data | 87 |
| 5.1 Introduction | 87 |
| 5.2 Multivariate Association | 88 |
| 5.3 The Proximity Function | 90 |
| 5.4 The Distance-based Bayes Allocation Rule | 91 |
| 5.5 Multivariate Multiple-Sample Tests | 92 |
| References | 96 |
| Part II Probability and Statistics | 98 |
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| 6 Empirical Bayes Assessment of the Hyperparameters in Bayesian Factor Analysis | 99 |
| 6.1 Introduction | 99 |
| 6.2 The BFA Model | 100 |
| 6.3 Assessing the Hyperparameters | 101 |
| 6.4 Bayesian Estimation of ., F, . | 103 |
| 6.5 Example | 105 |
| 6.6 Method Comparison and Summary | 108 |
| References | 109 |
| Part III Order Statistics and Analysis | 110 |
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| 7 Negative Mixtures, Order Statistics, and Systems | 111 |
| 7.1 Introduction | 111 |
| 7.2 Relationships between Mixtures and Systems | 112 |
| 7.3 Properties of Mixtures and Systems | 114 |
| 7.4 The Bridge Structure | 117 |
| Appendix | 120 |
| References | 121 |
| 8 Models of Ordered Data and Products of Beta Random Variables | 123 |
| 8.1 Introduction | 123 |
| 8.2 Intermediate Order Statistics and the Ordered Dirichlet Distribution | 125 |
| 8.3 Properties of Fractional Order Statistics | 127 |
| References | 128 |
| 9 Exact Inference and Optimal Censoring Scheme for a Simple Step- Stress Model Under Progressive Type- II Censoring | 129 |
| 9.1 Introduction | 129 |
| 9.2 Model Description and MLEs | 131 |
| 9.3 Conditional Distributions of the MLEs | 133 |
| 9.4 Confidence Intervals | 139 |
| 9.5 Simulation Study | 143 |
| 9.6 Optimal Censoring Scheme | 143 |
| 9.7 Illustrative Examples | 145 |
| 9.8 Conclusions | 147 |
| Appendix: Tables and Figures | 148 |
| References | 158 |
| Part IV Engineering Modeling | 160 |
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| 10 Non-Gaussian State Estimation in Power Systems | 161 |
| 10.1 Introduction | 161 |
| 10.2 Maximum Likelihood Estimation | 162 |
| 10.3 Transformation of Random Variables | 163 |
| 10.4 The Transformed Likelihood Estimation Problem | 166 |
| 10.5 General State Estimation (GSE) Formulation | 167 |
| 10.6 Bad Data Detection | 168 |
| 10.7 Illustrative Example | 168 |
| 10.8 Conclusions | 174 |
| References | 175 |
| 11 Statistics Applied to Wave Climate on a Beach Profile | 177 |
| 11.1 Introduction | 177 |
| 11.2 Offshore Wave Climate | 178 |
| 11.3 Local Wave Height Description | 181 |
| 11.4 Consecutive Wave Heights | 184 |
| 11.5 Maximum Wave Height | 186 |
| 11.6 Conclusions | 188 |
| References | 188 |
| Part V Extreme Value Theory | 189 |
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| 12 On Some Dependence Measures for Multivariate Extreme Value Distributions | 190 |
| 12.1 Introduction | 190 |
| 12.2 Dependence Coefficients | 191 |
| 12.3 Examples | 193 |
| 12.4 Relation between t1 and t2 | 195 |
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