Preface |
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ix | |
1. Univariate Extreme Value theory |
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1 | |
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1 | |
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1.1.1. Distribution of the smallest value |
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2 | |
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1.1.2. Distribution of the largest value |
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4 | |
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1.1.3. General distributions of order statistics |
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5 | |
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1.1.4. Plotting positions |
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9 | |
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1.2. Extreme Value theory |
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11 | |
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12 | |
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31 | |
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1.2.3. Scaling of extremes |
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39 | |
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1.2.4. Contagious Extreme Value distributions |
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50 | |
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1.3. Hazard, return period, and risk |
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53 | |
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58 | |
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1.4.2. Volcanic eruptions |
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66 | |
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68 | |
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72 | |
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77 | |
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83 | |
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1.4.7. Extreme sea levels and high waves |
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86 | |
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1.4.8. Low flows and droughts |
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89 | |
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94 | |
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106 | |
2. Multivariate Extreme Value theory |
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113 | |
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2.1. Multivariate Extreme Value distributions |
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114 | |
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2.2. Characterization of the domain of attraction |
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120 | |
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2.3. Multivariate dependence |
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123 | |
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2.4. Multivariate return periods |
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126 | |
3. Bivariate Analysis via Copulas |
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131 | |
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131 | |
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142 | |
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3.3. Return periods via copulas |
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148 | |
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3.3.1. Univariate vs. bivariate frequency analysis |
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150 | |
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155 | |
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157 | |
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3.3.4. Conditional return periods |
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159 | |
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3.3.5. Secondary return period |
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161 | |
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170 | |
4. Multivariate Analysis via copulas |
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177 | |
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4.1. Multivariate copulas |
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178 | |
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183 | |
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4.3. Conditional mixtures |
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186 | |
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4.3.1. The 3-Dimensional case |
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186 | |
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4.3.2. The 4-Dimensional case |
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189 | |
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190 | |
5. Extreme Value Analysis via Copulas |
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191 | |
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5.1. Extreme Value copulas |
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191 | |
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201 | |
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207 | |
Appendix A Simulation of Copulas |
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209 | |
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A.1. The 2-Dimensional case |
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209 | |
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212 | |
Appendix B Dependence |
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219 | |
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B.1. Bivariate concepts of dependence |
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219 | |
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B.1.1. Quadrant dependence |
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219 | |
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221 | |
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B.1.3. Stochastic monotonicity |
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223 | |
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B.1.4. Corner set monotonicity |
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224 | |
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B.1.5. Dependence orderings |
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225 | |
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B.1.6. Measure of dependence |
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225 | |
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B.2. Measures of association |
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227 | |
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B.2.1. Measures of concordance |
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227 | |
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228 | |
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230 | |
Appendix C Families of Copulas |
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233 | |
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233 | |
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C.2. The Gumbel-Hougaard family |
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236 | |
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237 | |
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C.4. The Ali-Mikhail-Haq (AMH) family |
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240 | |
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242 | |
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C.6. The Farlie-Gumbel-Morgenstern (FGM) family |
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244 | |
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247 | |
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248 | |
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C.10. The Hiisler-Reiss family |
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252 | |
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C.11. The Elliptical family |
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254 | |
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256 | |
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C.13. The Marshall-Olkin family |
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257 | |
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C.14. The Archimax family |
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264 | |
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C.15. Construction methods for copulas |
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264 | |
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C.15.1. Transformation of copulas |
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265 | |
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C.15.2. Composition of copulas |
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266 | |
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C.15.3. Copulas with given diagonal section |
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268 | |
References |
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271 | |
Index |
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285 | |
Glossary |
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291 | |