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

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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

Logistic distribution      358
Logistic distribution, BLUE in      364
Logistic distribution, estimation of parameters in      364
Logistic distribution, generalized      52
Logistic distribution, moments of Order statistics in      358
Logistic distribution, optimal spacing of Order statistics in      295
Logistic distribution, percentage points of Order statistics in      355
Lognormal distribution, estimation of parameters in      364
Lognormal distribution, moments of Order statistics in      358
Lognormal distribution, percentage points of Order statistics in      355
Lorenz curve      90—91
m-dependent processes      288 309—310
Majorization      103—104
Markov chain, order statistics as a      17—20 154 174
Markov chain, record values as a      31—32
Maxima, ratio of      178
Maxima, statistics expressible as      125—133 149—152
Maximum likelihood (ML) methods, for censoring and truncation      193—202
Maximum, $X_{(n)}$ , $X_{n:n}$ , $Y_{(n)}$ in multinomial      151
Maximum, $X_{(n)}$ , $X_{n:n}$ , $Y_{(n)}$ of exchangeable variates      102—103
Maximum, $X_{(n)}$ , $X_{n:n}$ , $Y_{(n)}$ , asymptotic distribution of      22 296
Maximum, $X_{(n)}$ , $X_{n:n}$ , $Y_{(n)}$ , bounds for moments of      60—63 119
Maximum, $X_{(n)}$ , $X_{n:n}$ , $Y_{(n)}$ , distribution of      26
Mean deviation, in normal samples      250
Mean deviation, robustness of      212
Median      2
Median absolute deviation (MAD)      223
Median Filter      141
Median for Cauchy distribution      54
Median in life testing      191
Median in normal samples      241—242 277
Median of pairwise means      215
Median, asymptotic properties      285 288
Median, confidence intervals for      159—162 362
Median, distribution of (n even)      28
Median, efficiency of      93 241—242
Median, moving      140
Median, multivariate      164 169
Median, percentage points for various populations      356
Median, population      5 45
Median, sample      2 23 241—243
Midmean      217 235—237
Midrange (=midpoint)      15
Midrange in uniform distribution      175 320
Midrange, asymptotic distribution of      326—327
Midrange, distribution of      26—27
Midrange, properties of      242
Minimum $X_{(1)}$ , $X_{1:n}$ , application of      284
Minimum $X_{(1)}$ , $X_{1:n}$ , asymptotic distributions of      303
Mode, estimation of      290
Moments of Order statistics      33—44 49—55
Moments of Order statistics, approximations for      70—74 83—86
Moments of Order statistics, bootstrap estimation of      183—5 227—228
Moments of Order statistics, bounds for      60—74
Moments of Order statistics, discrete case      42—44
Moments of Order statistics, existence of      34 54
Moments of Order statistics, normal case      40—42 53
Moments of Order statistics, recurrence relations between      44—49 55—58
Moments of Order statistics, relations between      38—39 49—52
Moments of Order statistics, tables of      356—360
Monte Carlo methods in robustness studies      217 223
Monte Carlo methods, Order statistics in      15 31
Moving order statistics      140—141
Multinomial distribution, maximum variate in      151
Multinomial distribution, moments of extremes      360
Multinomial distribution, range in      261—262
Multiple comparisons      3
Multiple comparisons based on range      253—256
Multiple decision procedures      3
Multivariate asymptotic distribution of Order statistics      313—315
Multivariate data, ordering of      13
Multivariate extreme deviate      131
Multivariate inequalities      133
Multivariate medians      164 169
Multivariate normal distribution      see also “Equicorrelated normal variates”
Multivariate normal distribution, censoring of      203
Multivariate normal distribution, Order statistics in      13 100—102
Multivariate tolerance regions      166
NBU, New better than used      76 90
NBUE: NBU in expectation      91
Negative binomial distribution      360
Nonparametric inference      159—170
Normal distribution      see also “Bivariate normal distribution”; “Multivariate normal distribution”
Normal distribution, asymptotic distribution of maximum in      302
Normal distribution, asymptotic estimation in      339—340
Normal distribution, bounds and approximations for $E(X_{r:n})$       80—86
Normal distribution, cdf of extremes in      355
Normal distribution, cdf of range in      356
Normal distribution, coefficients of BLUE in      363
Normal distribution, contaminated      360
Normal distribution, independence of mean and range      18—19
Normal distribution, linear estimators of $\mu$ and $\sigma$ for      189—190
Normal distribution, moments of Order statistics      40—42 356
Normal distribution, optimal spacing of Order statistics in      294—295 317
Normal distribution, percentage points of Order statistics in      355
Normal distribution, probability plotting for      270—271
Normal distribution, quick estimators of $\mu$ and $\sigma$ for      241—250
Normal distribution, robust estimation of $\mu$ and $\sigma$ for      211—216
Normal distribution, tests of      272—273 365
Notation      4—7
Optimal asymptotic estimation by Order statistics      335
Optimal choice (spacing) of Order statistics in large samples      290—296
Optimal choice (spacing) of Order statistics in large samples, tables for normal parent      366
Optimal choice (spacing) of Order statistics in large samples, tests under      296
Order statistics      see “Distribution of Order statistics” and under specific statistics and specific distributions
Order statistics, fractional      21 162
Order statistics, generalized      21—22
Orthonormal system      70
Outliers      3
Outliers, robust estimation in presence of      218—223 236—237
Outliers, tables of tests for      360—362
P-P plot      272
Pareto distribution      52
Pareto distribution, k-variate      117
Pareto distribution, moments of Order statistics in      52 360
Pareto distribution, optimal spacing of Order statistics in      295
Partial sums of concomitants      348 353
Peak to median ratio      27
Peakedness      77
Percentage points      see under specific statistics and specific distributions
Permanent (of a matrix)      98 113
Poisson distribution, range in      261—262
Pooled rms estimator of $\sigma^{2}$       121
Power-function distribution      52
Power-function distribution, characterization      157
Power-function distribution, optimal spacing of Order statistics in      295
Prediction, distribution-free intervals      167—169
Prediction, parametric intervals      208—211
Prediction, point predictors      209—211
Princeton study      217—218
Probability plotting      270—273 284
Q-Q plotting      270
Quality control      274—277
Quantile, density function      84
Quantile, differences      163—164
Quantile, function      5
Quantile, population      5
Quantile, sample      5
Quantiles, asymptotic (joint) distribution of      285—290 316 347
Quantiles, bootstrap estimation of      183—185 227—228
Quantiles, bounds for $E(X_{(r)})$ in terms of      80—83
Quantiles, distribution-free confidence intervals for      159—164 169—170
Quasi-midrange      242
Quasi-range      15
Quasi-range in estimation of $\sigma$       248 364—365
Quasi-range in normal samples      248—249 326 351 364
Quasi-range, moments of      356
Quasi-range, tables of cdf      356
Quenouille’s method      see “Jackknife”
Quick statistics      239—282 see

Random division of an interval      133—137 153—155
Random division of an interval, distribution of longest interval      135 154—155 362
RANGE      1
Range for discrete parent      30 261—262
Range in quality control      274—276
Range in short-cut methods      239—240 243—247 257—262 356
Range in uniform distribution      175
Range ratios, $max_{j}W/\Sigma_{j}W$       136 258 362
Range ratios, $W_{max}/W_{min}$       365
Range ratios, in normal distribution      257 365
Range ratios, in uniform distribution      27 363
Range to spot gross errors      247—248
Range, applications of      239—240
Range, approximations to      244—246
Range, asymptotic distribution of      324—326
Range, bivariate (extreme spread)      251
Range, bounds for moments of      64—65
Range, distribution of      13—14 26—27
Range, effect of nonnormality on      245 247
Range, efficiency of      240 243 277
Range, mean      244
Range, moments of      37 54 356—357
Range, moving      140—141 276
Range, noncentral      280
Range, power function of range tests      254—256 279—280
Range, recurrence relations for expected      56—57
Range, studentized      see “Studentized range”
Range, tables relating to      356
Range, variance of      54
Range, “thickened”      248—249 259
Rank-order statistics      3
Ranked-set sampling      262—267 280—281
Rate of convergence of $X_{(n)}$       302—303
Rate of convergence of L-statistics      334—335
Ratio of Order statistics      28
Rayleigh distribution      204 359 364
Rayleigh distribution, optimal spacing of Order statistics in      295
Record values      20—21 32 87 307 328
Rectangular distribution      see “Uniform distribution”
Recurrence relations between moments and cdf’s of Order statistics      23 44—49
Recurrence relations for Order statistics in non-iid variates      104—106
Regression coefficient, quick estimate of      251—252
Regression model, estimation of parameters in      202—203
Reliability      207—208
Robust estimation      211—223
Robust estimation in contaminated normal distribution      360
Robust estimation in presence of outliers      211 218—223
Robust estimation of mean of symmetric distributions      212—216
Robustness, lack of exponential in life testing      204
Robustness, lack of tests for homogeneity of variances      258
s-comparison      80 82—83
SCALE      see also “Location and scale parameters”
Scale, estimation in presence of outliers      222—223
Schwarz’s inequality      61 86
Scores      33
Selection differential      41—42 53 65 102 351—353
Selection differential, induced      144 348 353
Selection procedures      102 144
Sensitivity curve      218
Sequential, confidence intervals      164
Sequential, tests based on range      258 260
Serial correlation      136
Series system      90
Short-cut procedures      239—282
Short-cut procedures by optimal spacing of Order statistics      290
Short-cut procedures for discrete variates      281—282
Short-cut procedures for estimating dispersion      243—248
Short-cut procedures for estimating location      241—243
Short-cut procedures for tests in normal samples      257—261 365
Short-cut procedures in bivariate samples      250—253
Short-cut procedures, tables for      365
Signal processing      141
Simulation, Order statistics in      15 355
Sorting (ordering)      31 355
Spacings (differences between successive Order statistics)      64 134—136 138 153—154 187—188 273
Spacings from exponential distribution      18 113 142
Spacings of order m      136—137 290 341—342
Spacings, asymptotic distributions      154 308 319—320 327—328
Stable distributions      295
Star-shaped      76
Stein's test, range version of      260
Stochastic orderings      74—80
Stratified samples      164
Structural inference      192
Student's distribution, moments of Order statistics in      359
Studentization      121—124
Studentization, external      121
Studentization, internal      121
Studentized range      1 121—124
Studentized range in analysis of variance      253—256
Studentized range in multiple comparisons      253—256
Studentized range, bounds for internally      247—248
Studentized range, noncentral      256 280
Studentized range, tables      360—362
Sufficient statistics, Order statistics as      172
Superadditive      76—77
Symmetric distributions      22 36 50
Symmetric distributions, bounds for moments of Order statistics in      62—64
Symmetric distributions, estimation of location and scale parameters in      179—180
Symmetric distributions, robust estimation of mean of      211—218
Symmetric distributions, tests for      274
Symmetric power distribution      215
Systematic statistics = function of the order statistics      15
Tables      4 355—366
Time series      135 140—141
Tolerance (= breakdown point)      215—216
Tolerance intervals for normal distributions using range      276—277 366
Tolerance intervals in exponential distribution      234
Tolerance intervals, distribution-free      164—167 169 363
Total time on test, statistic      91 209 234—235
Total time on test, transform      91
Trimmed mean      51 213
Trimmed mean as robust estimator      213—216
Trimmed mean in Cauchy distribution      237
Trimmed mean in normal distribution      242
Trimmed mean, asymptotic distribution of      329—331 335
Truncated distributions, moments of Order statistics in      359
Truncated normal distribution, estimation for      193—194
Truncation, estimation of parameters in case of      191—194
Truncation, versus censoring      191—192
Tukey’s $\lambda$ -distributions      63—64
Tukey’s $\lambda$ -distributions in robustness studies      214 247
UMP tests based on Order statistics      178—179
UMVU estimators, Order statistics as      174—175
Unbiased nearly best linear estimator      191
Uniform distribution      14—15
Uniform distribution, censoring in      230 233
Uniform distribution, differences of Order statistics in      14
Uniform distribution, estimation of parameters of      173—177 224
Uniform distribution, hypothesis testing in      177—179 363
Uniform distribution, L-statistics in      139
Uniform distribution, midpoint in      26—27
Uniform distribution, moments of Order statistics in      35—36 356
Uniform distribution, percentage points of Order statistics in      355
Uniform distribution, random division of interval      133—135
Uniform distribution, range in      356 363
Uniform distribution, range ratio in      27 178 363
Unimodal distribution of Order statistics      23
Upper percentage points, of statistics expressible as maxima      125—127 361—362 see
Vandermonde’s theorem      129
Variance, analysis of      see “Analysis of variance”
Variances of Order statistics      34—35 see
Weibull distribution      364
Weibull distribution in asymptotic theory      284
Weibull distribution, estimation for      364
Weibull distribution, moments of Order statistics in      359
Weibull distribution, optimal spacing of Order statistics in      295
Weibull distribution, percentage points of Order statistics in      355
Whitworth      136
Wilcoxon’s test, relation to robust estimation      215

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