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

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

јвторы: David H., Nagaraja H.

јннотаци€:

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: en

–убрика: ћатематика/¬еро€тность/—татистика и приложени€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: Third Edition

√од издани€: 2003

 оличество страниц: 482

ƒобавлена в каталог: 28.05.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$F_{max}$      256Ч258 365
$PF_{2}$, Polya frequency function of order      2 78
$S_{max}^{2}/S_{0}^{2}$      132Ч133 362
$S_{max}^{2}/S_{min}^{2}$      256Ч258 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      216Ч218
Analysis of variance, by range methods      253Ч256 261 364Ч365
Applications general      1Ч3
Applications of extremes      284Ч285
Applications of range      239Ч240
Approximations for moments of Order statistics      70Ч74 83Ч86
Approximations to upper percentage points of statistics expressible as maxima      125Ч133
Asymptotic distribution for dependent variates      309Ч311
Asymptotic distribution for multivariate samples      313Ч315
Asymptotic distribution of concomitants of Order statistics      345Ч350
Asymptotic distribution of extremes      296Ч309
Asymptotic distribution of intermediate Order statistics      311Ч313
Asymptotic distribution of linear functions of Order statistics      331Ч335
Asymptotic distribution of midrange      326Ч327
Asymptotic distribution of quantiles      285Ч290
Asymptotic distribution of range      324Ч326
Asymptotic distribution of sample spacings      327Ч328
Asymptotic distribution of trimmed mean      329Ч331
Asymptotic estimation      335Ч341
Bahadur representation of sample quantile      285 288 311
BasuТs theorem      174 209
Bayesian methods      236
Bernoulli distribution      32 54Ч55 88
Best linear estimates      see УLinear estimatorsФ
Best linear unbiased (BLU) predictor      209Ч210
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      261Ч262 356
Bioequivalence      255
Bivariate distributions, estimation in      250Ч253 279
Bivariate distributions, Order statistics in      13 25 278
Bivariate exponential      102 117 321
Bivariate extremal distributions      313Ч315 321
Bivariate normal distribution, circular      250Ч251
Bivariate normal distribution, linear function of Order statistics in      114
Bivariate normal distribution, moments of Order statistics in      54
BlomТs estimates      191
blue      185Ч189 see
BLUE, tables of coefficients of      363Ч364
Bonferroni inequalities      126 133 152
Boole formula      125
Bootstrap estimation      183Ч185 227Ч228
Bounds for linear functions of Order statistics and their expectations      106Ч112 118
Bounds for moments of Order statistics      60Ч74
Bounds for upper percentage points of statistics expressible as maxima      125Ч133
c-comparison; c-ordering; c-precedence      79Ч82
Cauchy distribution      357
Cauchy distribution, median in      54
Cauchy distribution, moments of Order statistics in      57 357
Cauchy distribution, trimmed mean in      237
CauchyТs functional equation      142
CauchyТs functional equation, integrated      142
CauchyТs inequality      107 111
Censoring      191
Censoring, BLUE in presence of      363Ч364
Censoring, estimation in presence of      191Ч208 229Ч231 335Ч341
Censoring, in exponential distribution      204Ч208 232Ч235
Censoring, of multivariate normal      203
Censoring, progressive      200Ч201
Censoring, Type I      191Ч195
Censoring, Type II      191Ч208
Characterizations      142Ч144 156Ч158
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 УGamma distributionФ
Circular normal distribution      250Ч251
Closest two out of three observations      237
Clusters      137
Combinatorial extreme-value distributions      129
Completeness      173Ч175
Computer simulation, Order statistics in      15 355
Computing distribution of functions of Order statistics      355
Computing distribution of Order statistics in inid case      105Ч106
Concave-convex functions      82
Concomitants of Order statistics      144Ч148 158 251Ч253
Concomitants of Order statistics in double sampling      267Ч268
Concomitants of Order statistics in ranked-set sampling      263Ч264
Concomitants of Order statistics, asymptotic theory of      345Ч350 353
Conditional distribution of Order statistics      17
Confidence intervals for $\sigma$ in normal samples      257 365
Confidence intervals, distribution-free      159Ч164 169Ч170
Contamination      see УOutliersФ
control charts      274Ч276
Convex function      66 107
Correlation coefficient, quick estimate of      252
Covariances of Order statistics      34Ч35 50
Covariances of Order statistics, tables of      356Ч359
Covering circle      251
Data analysis      2 239
Data compression      3 290Ч296
Density-quantile function      84
Density-quantile function in asymptotic distribution of Order statistics      285Ч291 311Ч312 336Ч340
Dependent variates, asymptotic distribution of Order statistics      309Ч311
Dependent variates, bounds for expectations of L-statistics      106Ч112 118Ч119
Dependent variates, Order statistics in      99Ч102 114Ч117
Dependent variates, quantile-theory for      288
DFR, Decreasing failure rate      75 89
Differences of order statistics      13Ч14 26Ч29
Differences of order statistics in uniform distribution      14 133Ч137
Differences of order statistics, successive (spacings)      18 133Ч137 153Ч154 327Ч328
Dirichlet distribution      21 134
Discrete populations      see also under specific distributions
Discrete populations, distribution of Order statistics      16 19Ч20 29 31
Discrete populations, distribution of range      30
Discrete populations, quick tests in      261Ч262
Dispersion, measures of      243Ч250 278Ч279
Dispersion, smaller in      77Ч78
Distribution of Order statistics      9Ч32 see
Distribution of Order statistics for dependent variates      99Ч102 114Ч117
Distribution of Order statistics for discrete parent      16 29
Distribution of Order statistics for independent non-iid variates      96Ч99
Distribution of Order statistics, unimodality of      23
Distribution-free bounds for moments of Order statistics and range      59Ч74 86Ч89
Distribution-free confidence intervals for quantiles      159Ч164 169Ч170
Distribution-free prediction intervals      167Ч169
Distribution-free tolerance intervals      164Ч167 169
Domain of attraction (for extreme)      296Ч300 303 305
Domain of attraction (for extreme) in tail index estimation      341Ч344
Domain of attraction (for extreme), convergence of moments      305
Domain of attraction (for extreme), discrete parent      304
Double exponential (Laplace)      358 364
Double sampling      267Ч268
Duality principle      46Ч47
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 257Ч258
Equicorrelated normal variates      100Ч102 114Ч115
Equicorrelated normal variates, asymptotic distribution of maximum for      311
Equicorrelated normal variates, linear functions of      101 114Ч115
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      171Ч237
Estimation by Order statistics for censored data      191Ч208 230Ч234 363Ч364
Estimation by Order statistics for distributions with end-point(s) depending on unknown parameters      173Ч177 224Ч225
Estimation by Order statistics of extreme quantiles      342
Estimation by Order statistics, simplified      189Ч190 200
Exchangeable variates      47 102Ч103
Expected values      see УMoments of Order statisticsФ
Exponential distribution      17Ч18 22 26 52 142 157
Exponential distribution in life testing      204Ч208 232Ч234
Exponential distribution, asymptotic distribution of maximum in      22
Exponential distribution, bivariate (Marshall Ч Olkin)      102 117 207 321
Exponential distribution, characterization of      142Ч143 157Ч158
Exponential distribution, estimation of parameters of      204Ч208 232Ч235
Exponential distribution, L-statistics in      137Ч138
Exponential distribution, moments of Order statistics in      52
Exponential distribution, optimal spacing of Order statistics in      290Ч291 295
Exponential distribution, recurrence relation for      117
Exponential distribution, test of      273
Exponential distribution, tests in      205Ч206 232
Exponential distribution, truncated      57Ч58 359
Extremal      60
Extremal pdf      61Ч64
Extremal process      306
Extremal quotient      15 326
Extreme deviate      1 124Ч125
Extreme multivariate      131 362
Extreme studentized      149 324 361
Extreme, tables of cdf of      361
Extreme-value distribution(s) in asymptotic theory      283Ч285
Extreme-value distribution(s), bivariate      314Ч315 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      314Ч315
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      283Ч285 311 323
Extremes      1 see
Extremes, applications of      284Ч285
Extremes, asymptotic distribution of      296Ч309 317Ч321
Extremes, kth      306Ч307 319Ч320
Failure rate      75 204 see
Failure rate, increasing (IFR)      75 89Ч90
Finite population, Order statistics in      23 25 111 151 170 280
Fisher information (FI)      180Ч183 225Ч227
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      136Ч137
Gauss Ч Markov theorem      186
Generalized distance      96 292
Generalized Order statistics      21Ч22
Geometric distribution      22 32 235
Geometric range      326
GiniТs coefficient of concentration      140
GiniТs mean difference      249Ч250 253 269 273 279
GiniТs mean difference, asymptotic normality of      331 334
Goodness-of-fit tests, based on spacings      136Ч137 316Ч317
Goodness-of-fit tests, based on spacings and probability plotting      272Ч273 281Ч282
Goodness-of-fit tests, tables for      365
Graphical methods, half-normal plotting      273
Graphical methods, hazard plotting      274
Graphical methods, probability plotting      270Ч272
Greatest convex minorant      66
Greenwood statistic      136
Grouped data      201Ч202
GuptaТs simplified estimators      189Ч191
Half-normal distribution      see УChi (1 DF) distributionФ
Half-normal plotting      273Ч274
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
HoelderТs inequality      109
Homogeneity of variances      see УEquality of variancesФ
Hypothesis testing by Order statistics in exponential distribution      206
Hypothesis testing by Order statistics in normal distribution      257Ч261
Hypothesis testing by Order statistics in uniform distribution      177Ч179
IFR, Increasng failure rate      75 89Ч90
IFRA, Increasing failure rate average      76 89Ч90
Inclusion and exclusion, principle of      46 125Ч133
Independence results      18Ч19
Independence results for studentized statistics      123Ч124 148
Independence results, asymptotic      289Ч290 309 313 315
Inequalities for moments of Order statistics      see УBoundsФ
Inequalities for ordered sums      109Ч110
Inequality, Bonferroni      126
Inequality, Cauchy      107 111
Inequality, Hoelder      109
Inequality, Jensen      79
Inequality, Schwarz      61 85
Information in Order statistics      180Ч183
Inid (independent nonidentrically distributed) Order statistics in inid case      26 96Ч99 112Ч114
Intensity function      204 see
Intermediate Order statistics      311Ч313
Interquartile distance      163
Interval analysis      205
Interval hypothesis      255Ч256 364Ч365
Inverse cdf, approximations to moments of Order statistics by      80 see
Inverse Gaussian      358 363
JensenТs Inequality      79
k-out-of-n systems      2 97
kth extreme      306Ч307 319Ч320
Kurtosis, coefficient of      217 247
L-estimators      see УLinear estimatorsФ
L-moments      269 281
L-statistics      see УLinear functions of Order statisticsФ
Laplace distribution      358 364
Least-squares (LS) estimation of location and scale parameters      185Ч191
Legendre polynomials      51 71Ч73
Life testing      204Ч208
Likelihood ratio order      76 90
Linear estimators      171Ч172 see
Linear estimators by Gauss Ч Markov theorem      185Ч191 228Ч230
Linear estimators for censored data      191Ч204 230Ч231 363Ч364
Linear estimators for grouped data      201Ч202
Linear estimators for symmetric parent      188Ч189
Linear estimators in presence of outliers      218Ч223
Linear estimators, asymptotic theory of      331
Linear estimators, BlomТs      191
Linear estimators, miscellaneous      191
Linear estimators, robust      211Ч223 235Ч237
Linear estimators, simplified (Gupta)      189Ч190 200
Linear functions of Order statistics      33 see
Linear functions of Order statistics as estimators of scale and location parameters      185Ч208 228Ч234
Linear functions of Order statistics for equicorrelated normal variates      100Ч102 114Ч115
Linear functions of Order statistics in bivariate normal      114 140
Linear functions of Order statistics, asymptotic distribution of      331Ч335
Linear functions of Order statistics, bounds for      106Ч109 117Ч118
Linear functions of Order statistics, distribution of      137Ч140
Linear functions of Order statistics, optimal asymptotic estimation by      335
Linear functions of Order statistics, studentized      148Ч150
Linear programming      128
Lipschitz condition      333
LloydТs method of estimation by Order statistics      185Ч189 228Ч230
Location and scale parameters      see also УLinear estimatorsФ
Location and scale parameters for censored data      191Ч208 363Ч364
Location and scale parameters in uniform distribution      173Ч177 224
Location and scale parameters, estimation of      185Ч208
Location and scale parameters, quick measures of      241Ч243
Location and scale parameters, robust estimation of      211Ч223 235Ч237
Log-gamma distribution      364
Log-logistic distribution      364
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