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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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Предметный указатель
Multivariate, regular variation, limit function 167 Multivariate, regular variation, Poisson transform 179 Multivariate, regular variation, t-density 200 Multivariate, regular variation, tail probabilities 172 Negative drift 279-281 Networks, data 3 Neyman — Scott model 165 nice 48 360 nodes 254 Noncompliance 322 Norm 168 Normal dependence model 209 Normalization 324 325 One-point uncompactification 62 170-172 Oon/off process 3 125 Order statistics 99 110 114 Order statistics, conditional distribution 115 Order statistics, Markov chain 115 Order statistics, property 162 Order statistics, Renyi representation 115 PARETO 74 101 174 203 250 307 310 315 330 331 349 353 366 Parfit 10 Partial sum 214 247 Peaks over threshold 75 77 Peaks over threshold, multivariate 183 310 Pickands, estimator 90 93 350 368 Pickands, estimator, asymptotic normality 94 Pickands, estimator, consistent 94 Pickands, estimator, location/scale invariant 94 Pickands, estimator, properties 93 Pickands, plot 94 Pickands, plot, Danish data 105 Pickands, plot, exponential variates 96 Pickands, plot, Internet response data 104 Plots, altHill 317 364 Plots, Hill 4 317 319 364 Plots, parfit 366 Plots, Pickands 94 368 Plots, PP 102 Plots, pppareto 366 Plots, QQ 4 10 97 317 319 366 Plots, qqest 367 Plots, qqHill 368 Plots, smooHill 364 365 Plots, Starica 314 315 317 318 372 374 Plots, tail plot 104 Plots, time series 8 Point measure 50 Poisson, process 63 119 167 211 Poisson, process and extremal processes 160 Poisson, process and Levy processes 146 Poisson, process, augmentation 122 130 144 Poisson, process, cluster 164 Poisson, process, construction 143 163 Poisson, process, convergence to 194 Poisson, process, homogeneous 120 122 Poisson, process, Internet model 125 Poisson, process, Laplace functional 134 Poisson, process, marking 122 Poisson, process, nonhomogeneous 120 Poisson, process, order statistics property 162 Poisson, process, random measure 119 360 Poisson, process, rate 120 Poisson, process, thinning 162 Poisson, process, transform 138 167 179 210 Poisson, process, transform points 120 121 Poisson, process, transform points, examples 122 Poisson, process, transform, andm-dependence 210 Polar coordinates 168 169 172 177 194 197 238 313 324 335 337 339 Portmanteau theorem, probability measures 40 Portmanteau theorem, Radon measures 52 POT 74 75 77 101 Potter bounds 32 110 285 Potter bounds, variant 36 Price process 6 PRM 119 194 215 360 PRM, construction 163 PRM, Laplace functional 135 Probability integral transform 295 Product spaces 57 Products 231 236 250 355 Prohorov theorem 43 QQ, estimator 90 97 106 367 QQ, estimator, consistency 108 QQ, estimator, use least squares 106 QQ, plot 10 97 307 317 319 QQ, plot, 10 QQ, plot, BU data 4 QQ, plot, Danish data 105 QQ, plot, heavy tails 101 QQ, plot, Internet response data 102 103 QQ, plot, location-scale families 100 QQ, plot, looks bad 102 QQ, plot, method 98 QQ, plot, philosopy 97 QQ, plot, practice 108 QQ, plot, related plot, PP 102 QQ, plot, related plot, tail plot 104 Quantile, function 22 62 78 80 247 254 361 Quantile, sample 98 Quantile, theoretical 98 Queuing models 272 Radon 49 173 210 331 360 Random, closed sets 116 Random, measure 119 Random, walk 272 280 281 Ranks 310 312 313 315 316 318 332 335 371 374 Rate 316 ratio 241 Record 213 Rectangles 359 Regular variation 211 Regular variation and products 250 Regular variation at the origin 207 Regular variation, 37 Regular variation, composition 32 Regular variation, definition 20 Regular variation, differentiation 30 Regular variation, equivalences 232 Regular variation, equivalences, extremes converge 211 Regular variation, examples 21 35 Regular variation, exponent 20 Regular variation, global 204 248 312 342 345 Regular variation, hidden 322-325 327 328 330 333 337 351 Regular variation, integration 25 Regular variation, inversion 32 Regular variation, Karamata, representation 29 Regular variation, Karamata, theorem 25 Regular variation, marginal 204 311 312 Regular variation, measures 172 Regular variation, multivariate 322 Regular variation, nonstandard 203 204 236 309 Regular variation, nonstandard and products 236 Regular variation, nonstandard and sums 248 Regular variation, Potter bounds 32 Regular variation, properties 20 32 Regular variation, sequential form 22 Regular variation, slow variation 20 Regular variation, smooth version 33 Regular variation, standard 203 204 307 308 311 313 314 371 Regular variation, standard case 174 204 Regular variation, transformations 226 Regular variation, uniform convergence 24 Regular variation, vague convergence 61 Regular variation, von Mises condition 30 Reinsurance 13 Relative stability, slow variation 37 Relative stability, sums 37 Relatively compact 43 324 Relatively compact, vaguely 51 Renewal, epochs 265 Renewal, function 245 265 Renewal, process 245 273 Renyi representation 110 114 Response 316 317 Restriction 142 176 183 206 RETURNS 5—8 305—307 319 320 Reversed martingales 283 Sample, autocorrelation 341 Sample, variance 249 Scaling argument 57 83 338 Scaling property 314 Second converging together theorem 56 84 217 233 243 282 298 Second-order regular variation 67 94 292 302 304 Second-order regular variation, examples 67 Second-order regular variation, inversion 67 Self-similarity 124 154 Sessions 127 Skorohod, convergence, when impossible 69 Skorohod, metric 214 216 226 Skorohod, theorem 41 Skorohod, theorem, continuous mapping 43 Skorohod, topology 46 69 360 Slow, growth 255 Slow, variation 20 Slow, variation, relative stability 37 Slutsky’s theorem 55 181 347 Software 363 sources 254 Spacings 114 Stable, law 21 348 349 Stable, Levy motion 126 154 171 214 219 220 247 253 257 272 Stable, Levy motion, form of Levy measure 154 Stable, Levy motion, self-similarity 154 Stable, Levy motion, symmetric 154 Stable, Levy motion, weak convergence to 218 Stable, random variable 346—348 Stable, subordinator 247 347 Standard 7 Starica plot 314 315 318 372 374 Stochastic continuity 152 Stochastic differential equation 232 Stylized facts 5 8 Subordinator 153 Subordinator, characteristic function 153 Subordinator, stable 247 347 Subsequence principle 76 Supremum map 69 t-density 200 Tail, empirical measure 78 291 292 296 Tail, empirical process 291 Tail, equivalent 174 205 221 328 332 351 352 Tail, index 73 Tail, plot 104 The Simpsons 310 Thinning 162 Threshold 74 Threshold, selection 314 Throughput 238 316 Tightness 43 Time change 47 57 294 Time-series models 340 341 topology 170 324 Topology, destiny 324 Topology, locally uniform 45 Topology, Skorohod 46 69 Topology, uniform 46 Topology, vague 51 Total heaviosity v Totally skewed to the left 147 Totally skewed to the right 147 280 Traffic 4 125 253 Traffic, bursty 253 Traffic, cumulative 253 Traffic, intensity 273 275 Transformation of Poisson process 120 Transformation, addition 226 228 230 Transformation, augmentation 122 130 241 Transformation, binding 210 228 Transformation, idpolar 237 Transformation, Laplace 239 Transformation, linear combination 226 Transformation, point 120 Transformation, Poisson 179 Transformation, polar coordinate 168 169 313 339 Transformation, power 371 Transformation, prodid 238 Transformation, product 231 232 236 Transformation, rank 316 318 332 335 371 372 374 Transformation, ratio 241—243 Transformation, scaling 64 83 Transformation, standard 314 370 Transformation, thinning 162 Transition function and augmentation 144 Transmission rate 125 254 317 Uncompactification 170 Uncorrelated 6 9 Uniform, convergence 17 Uniform, metric 214 Uniform, topology 360 Unit sphere 169 Urysohn lemma 52 Vague metric 49 51 Vague metric, continuity with respect to 64 Vague metric, convergence 49 Value-at-risk 7 9 var 7 9 Vector notation 211 359 Version 155 Vervaat’s lemma 59 292 293 297 302 von Mises condition 30 300 303 Waiting time 273 274 279 Weak convergence 39 137 211—213 218 Weak convergence, converging together 55 Weak convergence, criterion 137 Weak convergence, Donsker’s theorem 54 Weak convergence, extremes 212 213 Weak convergence, inversion 58 Weak convergence, joint 83 Weak convergence, methods of proof 53 Weak convergence, methods of proof, characteristic function 53 Weak convergence, methods of proof, Cramer — Wold device 53 Weak convergence, methods of proof, Laplace transforms 53 Weak convergence, multivariate extremes 211 Weak convergence, Portmanteau theorem 40 Weak convergence, preservation under mappings 141 Weak convergence, PRMs 163 Weak convergence, product spaces 57 Weak convergence, properties 40 Weak convergence, relatively compact 43 Weak convergence, second converging together theorem 56 Weak convergence, Skorohod theorem 41 Weak convergence, Slutsky theorem 55 Weak convergence, stable Levy motion 218 Weak convergence, sums 221 Weak convergence, tightness 43 Weak convergence, Vervaat lemma 59 Yiddish haiku 314
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