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Resnick S.I. — Heavy-Tail Phenomena: Probabilistic and Statistical Modeling
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Название: Heavy-Tail Phenomena: Probabilistic and Statistical ModelingАвтор: Resnick S.I. Аннотация: This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of many phenomena where the probability of a single huge value impacts heavily. Record-breaking insurance losses, financial-log returns, files sizes stored on a server, transmission rates of files are all examples of heavy-tailed phenomena.
Язык: Рубрика: Технология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 404Добавлена в каталог: 13.05.2008Операции: Положить на полку |
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39 45 360 49 46 257 360 360 125 49 360 50 360 41 42 44 44 55 207 250 207 37 37 38 37 ACF 341 342 acf, classical 347 acf, heavy tailed 347 acf, sample 341 Active sources 254 Activity rate 264 Addition 226 228 Almost surely continuous 213 215 216 220 AltHill plot 317 Angular measure 179 196 211 251 304 308 310 311 313 316 318 337 352 370 Angular measure, full dependence 196 Angular measure, hidden 335 337 Angular measure, independence 193 arch 6 307 ARMA 341 Arzela — Ascoli theorem 46 Asymptotic dependence 304 Asymptotic dependence, full 195 Asymptotic independence 191 195 206 231 304 313 316 319 322 325 327 332 355 Asymptotic independence and extremes 209 Asymptotic independence, examples 209 Asymptotic independence, pairwise 209 Asymptotic normality 94 291 296 302 304 341 350 Asymptotic variance 90 369 Augmentation 122 130 144 241 Augmentation and transition functions 144 Autocorrelation function 8 341 Autoregressive model 184 341 Auxiliary function 37 axes 360 Basic convergence 138 Bellcore study 124 Big block–little block 210 Binding 210 228 Bootstrap 184 247 Bootstrap, asymptotics, do not work 189 Bootstrap, asymptotics, work 188 Bootstrap, multinomial 187 Bootstrap, procedure 187 Bootstrap, sample 187 188 Bootstrap, sample, mean 247 Bootstrap, sample, size 186 Boston University study 4 124 Breiman’s theorem 231 250 Breiman’s theorem, converse 250 Brownian motion 292 300 Brownian motion, convergence to 54 Cadlag 360 Cauchy 21 67 198 Characteristic function 53 153 154 Characteristic function, stable Levy motion 154 Choice theory 251 Cluster 164 Coefficient of tail dependence 322 327 Compact 171 324 Compact, support 360 Compactness condition 141 177 232 241 242 248 Complete randomness 120 Complete randomness and independent increments 151 composition 297 338 Cone 167 175 198 323 331 351 352 355 360 Cone, subcone 323 Connection rate 253 254 Consistent estimator 73 89 94 108 138 308 Continuous function, modulus of continuity 46 Continuous mapping 42 55 82 83 137 213 215 337 Continuous mapping, second theorem 69 Convergence, almost sure 41 Convergence, criterion, Laplace functional 137 Convergence, probability measures 39 Convergence, Skorohod 47 Convergence, uniform 17 Convergence, vague 49 Convergence, vague and regular variation 61 Convergence, weak 39 Convergence, weak and almost sure 41 Convex hull 251 Correlation 306 Cramer — Wold device 53 C[0, 1] 45 D(h) 42 Danish data 13 105 Data, networks 3 Data, transmission 123 Decoupage de Levy 76 115 Diffusion approximation 272 Domain of attraction 92 Domain of attraction, regular variation 23 Donsker’s theorem 54 292 Download time 264 Duration 238 316 D[0, 1] 46 Empirical measure 63 134 138 Empirical measure, convergence to PRM 138 Empirical measure, Laplace functional 139 Empirical measure, Poissonized 134 Empirical measure, weak convergence of 138 Exceedance 74 75 171 Exceedance, times 75 Excess 75 exchange rates 7 305 Extremal process 160 212 213 247 Extremal process and Levy process 164 Extremal process, construction 161 Extremal process, properties 161 Extremal process, structure 213 Extremal process, weak convergence 213 Extreme events 304 Extreme-value distributions 92 369 Extreme-value distributions, definition 91 Extreme-value distributions, domain of attraction 92 Extremes 171 211 363 368 Extremes, multivariate 211 212 Extremes, weak convergence 211 212 Fast growth 255 file size 238 253 317 First-come-first-served basis 273 Fractional Brownian motion 125 254 Function class, 207 250 Functional 213 215 220 Functional, difference 216 Functional, extreme 213 Functional, integral 84 Functional, largest jump 164 220 Functional, maximal 146 Functional, restriction 176 183 206 215 233 243 Functional, summation 146 214 215 Functional, summation, continuity 221 G 44 GARCH 6 307 GI/G/1 queue 272 278 281 Glivenko — Cantelli theorem 182 Hausdorff metric 251 Heavy tails and file size 125 Heavy tails and long-range dependence 125 130 Heavy tails and transmission duration 125 Heavy tails, analysis 1 Heavy tails, components 1 Heavy tails, context 3 Heavy tails, detection 96 101 102 Heavy tails, examples 3 Heavy tails, overview 1 Heavy traffic 254 272 275 279 Hidden regular variation 322—325 327 328 330 332 333 337 351 Hidden regular variation, detection 332 Hidden regular variation, example 330 331 Hidden regular variation, finite angular measure 331 352 353 Hidden regular variation, infinite angular measure 330 354 Hill estimator 74 80 85 187 292 296 302 303 350 364 369 Hill estimator, consistency 81 Hill estimator, Internet response data 102 Hill estimator, not location invariant 88 Hill estimator, practice 85 Hill estimator, variants, smooHill 89 Hill estimator, variants, smooHill, altHill 90 Hill plot 85 307 317 319 332 Hill plot, BU data 4 Hill plot, Danish data 105 Hill plot, exponential variates 96 Hill plot, horror 86 Hill plot, Internet response data 103 Hill process 90 Homogeneous Poisson process 293 Independent increments 120 151 Induced measure 121 Infinite-node Poisson model 4 123 125 253 Infinite-node Poisson model and long-range dependence 127 Infinite-node Poisson model, active sources 254 Infinite-node Poisson model, fast growth 255 Infinite-node Poisson model, input rate 255 Infinite-node Poisson model, slow growth 255 Infinite-node Poisson model, transmission rate 123 254 Infinite-order moving average 341 Input rate 255 Insurance 13 319 332 Insurance, claims 264 319 Insurance, premium 13 Insurance, reinsurance 13 Internet 238 316 Internet, duration 124 125 316 Internet, file transfers 316 Internet, rate 124 316 Internet, response 102 316 317 Internet, size 124 317 Internet, throughput 316 Internet, traffic 123 Invariant 126 Inverse 18 360 inversion 32 58 266 Inversion, second-order regular variation 67 Ito representation 216 Karamata, representation 29 256 Karamata, theorem 25 85 132 219 246 258 261 262 285 299 Karamata, theorem and point processes 248 Karamata, theorem, stochastic version 207 Karamata, theorem, Tauberian 265 Karamata, theorem, variant 36 Kolmogorov, convergence criterion 150 Kolmogorov, inequality 157 160 218 283 Kolmogorov, inequality, continuous-time version 157 Laplace functional 132 190 210 287 Laplace functional and random measures 132 Laplace functional and weak convergence 137 Laplace functional, definition 132 Laplace functional, determines distribution 133 Laplace functional, empirical measure 139 Laplace functional, examples 134 163 Laplace functional, muscle flexing 137 Laplace functional, Poisson process 134 Laplace transform 37 53 79 239 272 Least squares 106 Levy, measure 214 219 249 279 280 Levy, measure, definition 146 Levy, process 146 171 214 280 Levy, process and Poisson process 146 Levy, process, characteristic function 151 155 Levy, process, compound Poisson 147 Levy, process, construction 146 150 Levy, process, independent increments 151 Levy, process, Ito representation 150 216 Levy, process, path properties 155 Levy, process, properties 150 Levy, process, stable Levy motion 154 Levy, process, stationary increments 152 Levy, process, stochastic continuity 152 Levy, process, subordinators 153 Levy, process, totally skewed 147 Levy, process, variance calculations 148 Levy, process, weak convergence 214 Levy, stable motion 218 Limit, function 167 Limit, function, continuity 210 Limit, measure 173 179 251 308 310 314 328 352 Limit, measure, general representation 196 Lindley queues 272 273 275 276 279 Linear process 341 Local uniform convergence 214 216 Log-gamma 68 Long-range dependence 4 6 123 253 254 Long-range dependence and heavy tails 125 126 130 Long-range dependence and religion 126 Long-range dependence, definition 126 Long-range dependence, detection 127 Long-range dependence, example 127 Long-range dependence, Internet traffic 123 Long-range dependence, packet counts per time 124 m-dependence 210 Marking, location dependent 144 Martingale 283 Max-infinite divisibility 161 Maximal inequality 283 Maximum-likelihood estimation 74 Mean measure 119 Metric, Hausdorff 116 Metric, Skorohod 46 214 Metric, space 360 Metric, space, cadlag functions 40 46 Metric, space, closed sets 116 Metric, space, continuous functions 40 45 Metric, space, Euclidean 44 Metric, space, examples 44 Metric, space, point measures 40 48 Metric, space, Radon measures 40 48 Metric, space, sequences 45 Metric, uniform 45 214 Metric, vague 49 Mittag — Leffler distribution 272 277 278 Mixtures 330 Modulus of continuity 46 55 Moment estimator 90 93 369 MSFT 113 Multivariate, heavy tails 304 322 Multivariate, regular variation 167 179 212 231 236 308 331 353 Multivariate, regular variation, asymptotic, full dependence 195 Multivariate, regular variation, asymptotic, independence 191 Multivariate, regular variation, Cauchy 198 Multivariate, regular variation, densities 199 Multivariate, regular variation, examples 191 198 200 Multivariate, regular variation, functions 167 Multivariate, regular variation, general construction 197 Multivariate, regular variation, independence 191
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