David H., Nagaraja H. — Order Statistics (Wiley Series in Probability and Statistics) :: Электронная библиотека попечительского совета мехмата МГУ

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

Авторизация

Поиск по указателям

David H., Nagaraja H. — Order Statistics (Wiley Series in Probability and Statistics)

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Order Statistics (Wiley Series in Probability and Statistics)

Авторы: David H., Nagaraja H.

Аннотация:

Covering both finite-sample theory and asymptotic theory, this volume explains the application procedures for many data-analysis techniques and quality control. Attention is given to shortcut methods, robust estimation, life testing, reliability, L-statistics, and extreme-value theory. An appendix provides a guide to related tables and computer algorithms. David taught statistics at Iowa State University; Nagaraja teaches statistics and internal medicine at The Ohio State University.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Edition

Год издания: 2003

Количество страниц: 482

Добавлена в каталог: 28.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$F_{max}$       256—258 365
$PF_{2}$ , Polya frequency function of order      2 78
$S_{max}^{2}/S_{0}^{2}$       132—133 362
$S_{max}^{2}/S_{min}^{2}$       256—258 365
$S_{max}^{2}/\sum_{t}S^{2}$       153 258 362
$TP_{2}$ (totally positive of order 2)      25
$W_{max}$ / $W_{min}$       365
Adaptive estimators      216—218
Analysis of variance, by range methods      253—256 261 364—365
Applications general      1—3
Applications of extremes      284—285
Applications of range      239—240
Approximations for moments of Order statistics      70—74 83—86
Approximations to upper percentage points of statistics expressible as maxima      125—133
Asymptotic distribution for dependent variates      309—311
Asymptotic distribution for multivariate samples      313—315
Asymptotic distribution of concomitants of Order statistics      345—350
Asymptotic distribution of extremes      296—309
Asymptotic distribution of intermediate Order statistics      311—313
Asymptotic distribution of linear functions of Order statistics      331—335
Asymptotic distribution of midrange      326—327
Asymptotic distribution of quantiles      285—290
Asymptotic distribution of range      324—326
Asymptotic distribution of sample spacings      327—328
Asymptotic distribution of trimmed mean      329—331
Asymptotic estimation      335—341
Bahadur representation of sample quantile      285 288 311
Basu’s theorem      174 209
Bayesian methods      236
Bernoulli distribution      32 54—55 88
Best linear estimates      see “Linear estimators”
Best linear unbiased (BLU) predictor      209—210
Beta distribution      6
Beta distribution bounds for $E(X_{r:n})$       92
Binomial distribution, moments of Order statistics in      44 360
Binomial distribution, range in      261—262 356
Bioequivalence      255
Bivariate distributions, estimation in      250—253 279
Bivariate distributions, Order statistics in      13 25 278
Bivariate exponential      102 117 321
Bivariate extremal distributions      313—315 321
Bivariate normal distribution, circular      250—251
Bivariate normal distribution, linear function of Order statistics in      114
Bivariate normal distribution, moments of Order statistics in      54
Blom’s estimates      191
blue      185—189 see
BLUE, tables of coefficients of      363—364
Bonferroni inequalities      126 133 152
Boole formula      125
Bootstrap estimation      183—185 227—228
Bounds for linear functions of Order statistics and their expectations      106—112 118
Bounds for moments of Order statistics      60—74
Bounds for upper percentage points of statistics expressible as maxima      125—133
c-comparison; c-ordering; c-precedence      79—82
Cauchy distribution      357
Cauchy distribution, median in      54
Cauchy distribution, moments of Order statistics in      57 357
Cauchy distribution, trimmed mean in      237
Cauchy’s functional equation      142
Cauchy’s functional equation, integrated      142
Cauchy’s inequality      107 111
Censoring      191
Censoring, BLUE in presence of      363—364
Censoring, estimation in presence of      191—208 229—231 335—341
Censoring, in exponential distribution      204—208 232—235
Censoring, of multivariate normal      203
Censoring, progressive      200—201
Censoring, Type I      191—195
Censoring, Type II      191—208
Characterizations      142—144 156—158
Chi (1 DF) distribution      357
Chi (1 DF) distribution, estimation for      363
Chi (1 DF) distribution, moments of Order statistics in      357
Chi (1 DF) distribution, percentage points of Order statistics in      355
Chi-squared distribution      see “Gamma distribution”
Circular normal distribution      250—251
Closest two out of three observations      237
Clusters      137
Combinatorial extreme-value distributions      129
Completeness      173—175
Computer simulation, Order statistics in      15 355
Computing distribution of functions of Order statistics      355
Computing distribution of Order statistics in inid case      105—106
Concave-convex functions      82
Concomitants of Order statistics      144—148 158 251—253
Concomitants of Order statistics in double sampling      267—268
Concomitants of Order statistics in ranked-set sampling      263—264
Concomitants of Order statistics, asymptotic theory of      345—350 353
Conditional distribution of Order statistics      17
Confidence intervals for $\sigma$ in normal samples      257 365
Confidence intervals, distribution-free      159—164 169—170
Contamination      see “Outliers”
control charts      274—276
Convex function      66 107
Correlation coefficient, quick estimate of      252
Covariances of Order statistics      34—35 50
Covariances of Order statistics, tables of      356—359
Covering circle      251
Data analysis      2 239
Data compression      3 290—296
Density-quantile function      84
Density-quantile function in asymptotic distribution of Order statistics      285—291 311—312 336—340
Dependent variates, asymptotic distribution of Order statistics      309—311
Dependent variates, bounds for expectations of L-statistics      106—112 118—119
Dependent variates, Order statistics in      99—102 114—117
Dependent variates, quantile-theory for      288
DFR, Decreasing failure rate      75 89
Differences of order statistics      13—14 26—29
Differences of order statistics in uniform distribution      14 133—137
Differences of order statistics, successive (spacings)      18 133—137 153—154 327—328
Dirichlet distribution      21 134
Discrete populations      see also under specific distributions
Discrete populations, distribution of Order statistics      16 19—20 29 31
Discrete populations, distribution of range      30
Discrete populations, quick tests in      261—262
Dispersion, measures of      243—250 278—279
Dispersion, smaller in      77—78
Distribution of Order statistics      9—32 see
Distribution of Order statistics for dependent variates      99—102 114—117
Distribution of Order statistics for discrete parent      16 29
Distribution of Order statistics for independent non-iid variates      96—99
Distribution of Order statistics, unimodality of      23
Distribution-free bounds for moments of Order statistics and range      59—74 86—89
Distribution-free confidence intervals for quantiles      159—164 169—170
Distribution-free prediction intervals      167—169
Distribution-free tolerance intervals      164—167 169
Domain of attraction (for extreme)      296—300 303 305
Domain of attraction (for extreme) in tail index estimation      341—344
Domain of attraction (for extreme), convergence of moments      305
Domain of attraction (for extreme), discrete parent      304
Double exponential (Laplace)      358 364
Double sampling      267—268
Duality principle      46—47
EDA (exploratory data analysis)      239
Efficiency      see relevant statistic
Elementary coverages      134 167
entropy      91
Equality of variances, tables for test of      362 365
Equality of variances, tests of      136 153 257—258
Equicorrelated normal variates      100—102 114—115
Equicorrelated normal variates, asymptotic distribution of maximum for      311
Equicorrelated normal variates, linear functions of      101 114—115
Equicorrelated normal variates, maximum in modulus of      360
Equicorrelated normal variates, maximum of      360
Equicorrelated normal variates, range of      101
Equicorrelated normal variates, studentized maximum of      361
Estimation by Order statistics      171—237
Estimation by Order statistics for censored data      191—208 230—234 363—364
Estimation by Order statistics for distributions with end-point(s) depending on unknown parameters      173—177 224—225
Estimation by Order statistics of extreme quantiles      342

Estimation by Order statistics, simplified      189—190 200
Exchangeable variates      47 102—103
Expected values      see “Moments of Order statistics”
Exponential distribution      17—18 22 26 52 142 157
Exponential distribution in life testing      204—208 232—234
Exponential distribution, asymptotic distribution of maximum in      22
Exponential distribution, bivariate (Marshall — Olkin)      102 117 207 321
Exponential distribution, characterization of      142—143 157—158
Exponential distribution, estimation of parameters of      204—208 232—235
Exponential distribution, L-statistics in      137—138
Exponential distribution, moments of Order statistics in      52
Exponential distribution, optimal spacing of Order statistics in      290—291 295
Exponential distribution, recurrence relation for      117
Exponential distribution, test of      273
Exponential distribution, tests in      205—206 232
Exponential distribution, truncated      57—58 359
Extremal      60
Extremal pdf      61—64
Extremal process      306
Extremal quotient      15 326
Extreme deviate      1 124—125
Extreme multivariate      131 362
Extreme studentized      149 324 361
Extreme, tables of cdf of      361
Extreme-value distribution(s) in asymptotic theory      283—285
Extreme-value distribution(s), bivariate      314—315 321
Extreme-value distribution(s), estimation of parameters of      204 297
Extreme-value distribution(s), generalized      297 357
Extreme-value distribution(s), moments of Order statistics in      357
Extreme-value distribution(s), multivariate      314—315
Extreme-value distribution(s), optimal spacing of Order statistics in      295
Extreme-value distribution(s), probability plotting for      271
Extreme-value distribution(s), three types of      296 303
Extreme-value theory      283—285 311 323
Extremes      1 see
Extremes, applications of      284—285
Extremes, asymptotic distribution of      296—309 317—321
Extremes, kth      306—307 319—320
Failure rate      75 204 see
Failure rate, increasing (IFR)      75 89—90
Finite population, Order statistics in      23 25 111 151 170 280
Fisher information (FI)      180—183 225—227
Folded normal distribution      363
Force of mortality      204 see
Fractional Order statistics      21 162
Gamma distribution      91
Gamma distribution, bounds for $E(X_{r:n})$       92
Gamma distribution, L-statistics in      139
Gamma distribution, moments of Order statistics in      357
Gamma distribution, optimal spacing of Order statistics in      295
Gamma distribution, percentage points of Order statistics in      355
Gaps of order m      136—137
Gauss — Markov theorem      186
Generalized distance      96 292
Generalized Order statistics      21—22
Geometric distribution      22 32 235
Geometric range      326
Gini’s coefficient of concentration      140
Gini’s mean difference      249—250 253 269 273 279
Gini’s mean difference, asymptotic normality of      331 334
Goodness-of-fit tests, based on spacings      136—137 316—317
Goodness-of-fit tests, based on spacings and probability plotting      272—273 281—282
Goodness-of-fit tests, tables for      365
Graphical methods, half-normal plotting      273
Graphical methods, hazard plotting      274
Graphical methods, probability plotting      270—272
Greatest convex minorant      66
Greenwood statistic      136
Grouped data      201—202
Gupta’s simplified estimators      189—191
Half-normal distribution      see “Chi (1 DF) distribution”
Half-normal plotting      273—274
Harmonic analysis      135 362
Hazard plotting      274
Hazard rate      75 204
Hazard rate, ordering      75 90
Historical references, L-statistics      331
Historical references, method of inclusion and exclusion      130
Historical references, outliers      107
Historical references, robustness      212
Hoelder’s inequality      109
Homogeneity of variances      see “Equality of variances”
Hypothesis testing by Order statistics in exponential distribution      206
Hypothesis testing by Order statistics in normal distribution      257—261
Hypothesis testing by Order statistics in uniform distribution      177—179
IFR, Increasng failure rate      75 89—90
IFRA, Increasing failure rate average      76 89—90
Inclusion and exclusion, principle of      46 125—133
Independence results      18—19
Independence results for studentized statistics      123—124 148
Independence results, asymptotic      289—290 309 313 315
Inequalities for moments of Order statistics      see “Bounds”
Inequalities for ordered sums      109—110
Inequality, Bonferroni      126
Inequality, Cauchy      107 111
Inequality, Hoelder      109
Inequality, Jensen      79
Inequality, Schwarz      61 85
Information in Order statistics      180—183
Inid (independent nonidentrically distributed) Order statistics in inid case      26 96—99 112—114
Intensity function      204 see
Intermediate Order statistics      311—313
Interquartile distance      163
Interval analysis      205
Interval hypothesis      255—256 364—365
Inverse cdf, approximations to moments of Order statistics by      80 see
Inverse Gaussian      358 363
Jensen’s Inequality      79
k-out-of-n systems      2 97
kth extreme      306—307 319—320
Kurtosis, coefficient of      217 247
L-estimators      see “Linear estimators”
L-moments      269 281
L-statistics      see “Linear functions of Order statistics”
Laplace distribution      358 364
Least-squares (LS) estimation of location and scale parameters      185—191
Legendre polynomials      51 71—73
Life testing      204—208
Likelihood ratio order      76 90
Linear estimators      171—172 see
Linear estimators by Gauss — Markov theorem      185—191 228—230
Linear estimators for censored data      191—204 230—231 363—364
Linear estimators for grouped data      201—202
Linear estimators for symmetric parent      188—189
Linear estimators in presence of outliers      218—223
Linear estimators, asymptotic theory of      331
Linear estimators, Blom’s      191
Linear estimators, miscellaneous      191
Linear estimators, robust      211—223 235—237
Linear estimators, simplified (Gupta)      189—190 200
Linear functions of Order statistics      33 see
Linear functions of Order statistics as estimators of scale and location parameters      185—208 228—234
Linear functions of Order statistics for equicorrelated normal variates      100—102 114—115
Linear functions of Order statistics in bivariate normal      114 140
Linear functions of Order statistics, asymptotic distribution of      331—335
Linear functions of Order statistics, bounds for      106—109 117—118
Linear functions of Order statistics, distribution of      137—140
Linear functions of Order statistics, optimal asymptotic estimation by      335
Linear functions of Order statistics, studentized      148—150
Linear programming      128
Lipschitz condition      333
Lloyd’s method of estimation by Order statistics      185—189 228—230
Location and scale parameters      see also “Linear estimators”
Location and scale parameters for censored data      191—208 363—364
Location and scale parameters in uniform distribution      173—177 224
Location and scale parameters, estimation of      185—208
Location and scale parameters, quick measures of      241—243
Location and scale parameters, robust estimation of      211—223 235—237
Log-gamma distribution      364
Log-logistic distribution      364

1 2 3

О проекте