Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Resnick S.I. — Heavy-Tail Phenomena: Probabilistic and Statistical Modeling
Resnick S.I. — Heavy-Tail Phenomena: Probabilistic and Statistical Modeling

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Heavy-Tail Phenomena: Probabilistic and Statistical Modeling

Автор: 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.

Key features:

* Unique text devoted to heavy-tails

* Emphasizes both probability modeling and statistical methods for fitting models. Most treatments focus on one or the other but not both

* Presents broad applicability of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology

* Clear, efficient and coherent exposition, balancing theory and actual data to show the applicability and limitations of certain methods

* Examines in detail the mathematical properties of the methodologies as well as their implementation in Splus or R statistical languages

* Exposition driven by numerous examples and exercises

Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 404

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$C(\mathbb{S})$      39
$C[0, \infty)$      45 360
$C^+_K(E)$      49
$D[0,\infty)$      46 257 360
$J_1$-topology      360
$M/G/\infty$ input model      125
$M_+(\mathbb{E})$      49 360
$M_p(\mathbb{E})$      50 360
$\mathbb{L}\mathbb{E}\mathbb{B}$      41
$\mathcal{C}(h)$      42
$\mathcal{F}$      44
$\mathcal{K}$      44
$\omega_{\delta}(f)$      55
$\prod$      207 250
$\prod$-variation      207
$\prod$-variation and regular variation      37
$\prod$-variation, auxiliary function      37
$\prod$-variation, composition      38
$\prod$-variation, definition      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, $\prod$      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
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте