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Stone C.J.D. — Course in Probability and Statistics
Stone C.J.D. — Course in Probability and Statistics

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Название: Course in Probability and Statistics

Автор: Stone C.J.D.

Аннотация:

This author's modern approach is intended primarily for graduate-level mathematical statistics or statistical inference courses. The author takes a finite-dimensional functional modeling viewpoint (in contrast to the conventional parametric approach) to strengthen the connection between statistical theory and statistical methodology.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 838

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceptance region      340 367
Addition, stepwise      558
Additive function      417
Additivity      20 571—572
Additivity of the sample distribution      10
Additivity, countable      20
Allowable levels      411
Alternative hypothesis      366
Analysis of variance      392
ANOVA table      392
Approximation      64
Approximation, best linear      318
Approximation, least-squares      474
Approximation, normal      149
Asymptotic correlation      725
Asymptotic covariance      725
Asymptotic standard deviation (ASD)      637 640 726
Asymptotic vanance-covariance matrix      725
Asymptotic variance (AV)      637 640 726
At random      15
Averages, law of      113
Basis      430
Basis functions, stepwise addition and deletion of      558
Basis, change of      433—437
Basis, orthogonal      461
Basis, orthonormal      461
Bayes' estimate      331
Bayes' theorem      282—284
Beetle experiment      682—683 744—745
Beetle experiment, data      682—683
Bernoulli distribution      36
Bernoulli distribution as binomial distribution      173
Bernoulli distribution, mean      82
Bernoulli distribution, probability function      36
Bernoulli distribution, second moment      99
Bernoulli distribution, standard deviation      101
Bernoulli distribution, variance      101
Best linear unbiased estimate (BLUE)      219
Beta distribution      141—143
Beta distribution, defined      141
Beta distribution, density function      141
Beta distribution, distribution function      187
Beta distribution, mean      143
Beta distribution, Mode      142
Beta distribution, second moment      143
Beta distribution, uniform distribution as      142
Beta distribution, variance      143
beta function      142
Beta-binomial distribution      337
Beta-binomial distribution, mean      337
Beta-binomial distribution, probability function      332
Between sum of squares (BSS)      391
Bias      114
Biased estimate      115
Binomial distribution      172—188 768—769
Binomial distribution as exponential family      662
Binomial distribution, Bernoulli distribution as      173
Binomial distribution, defined      173
Binomial distribution, exact P-values and      651—661
Binomial distribution, maximum-likelihood estimation and      688—689
Binomial distribution, mean      173
Binomial distribution, modes      176
Binomial distribution, Newton — Raphson method and      717—721
Binomial distribution, normal approximation to      179—186
Binomial distribution, Poisson approximation to      200—201
Binomial distribution, probability function      173 176 187
Binomial distribution, standard deviation      173
Binomial distribution, variance      173
Binomial formula      167
Binomial one-sample and multisample models      636
Bivariate normal distribution      272
Bivariate normal distribution, conditional distribution      323
Bivariate normal distribution, density function      272
Blocking      385 620—634
Bounded random variable      96
Box — Mueller method      261
Box, George, E.P.      407 605
Canonical parameter      635 663
Canonical regression function      673 674 675
Canonical regression function, maximum-likelihood estimate of      699—707 789—790
Canonical regression model      675
Canonical regression model, experimental version      679—681 788—789
Canonical regression model, input-response version      675—679 787—788
Canonical regression model, linear      677
Cardinality      3 6
Cartesian product      7
Cauchy distribution      51 68.
Causal model      325
Causation      324—329
Causation, correlation vs.      324 327 328
Central limit theorem      158—160
Change of basis      433—437
Change of basis, coefficient matrix for      434
Chebyshev's inequality      111
Chi-square distribution      344—346 774
Chi-square distribution as gamma distribution      345
Chi-square distribution, defined      344
Chi-square distribution, density function      345
Chi-square distribution, distribution function      345
Chi-square distribution, mean      345
Chi-square distribution, normal approximation to      345
Chi-square distribution, quantiles      345 831
Chi-square distribution, standard deviation      345
Chi-square distribution, variance      345
Cholesky decomposition      264 273 757
choose      165
Clustering      290
Coded value      396
Coefficient      430
Coefficient correlation      215
Coefficient matrix for change of basis      434
Coefficient multiple correlation      508
Coefficient of variation      106
Coefficient regression      416
Coefficient vector      430
Collinear design points      441
Combination      165
Combinatorics      162—172
Complement      5
Complete factorial experiment      407 412
Completely randomized design      622
Completely randomized design, improving      628
Compound experiment      9—12
Conditional density function      300—307
Conditional density function, defined      301—302
Conditional distribution      274—285
Conditional distribution of discrete random variables      278—282
Conditional distribution, defined      275
Conditional distribution, mean of      302 308
Conditional distribution, standard deviation of      302 308
Conditional distribution, variance of      302 308
Conditional expectation      307—316
Conditional expectation, defined      308
Conditional probability      275
Conditional probability function      283—284
Conditional probability, Bayes' theorem and      282
Conditional variance      308
Conditioning      274—337
Conditioning, multivariate normal distribution and      322—330
Conditioning, sampling without replacement and      285—292
Confidence bound      358—359 522
Confidence bound, nominal      642 729
Confidence interval      339 343 359 522
Confidence interval, nominal      642 729
Confounder      326
Confounding      328
Congruential method      126
Consistent estimate      1 15
Constancy, test of      573—574
Constant function      427
Constant random variable      33
Constant random variable, mean      82
Constant random variable, standard deviation      101
Constant random variable, variance      101
Constant weights      455
Continuous distribution      38
Continuous random variable      38 87—90
Coplanar design points      442
Coronary heart disease study      683 730—732 747—748
Coronary heart disease study, data      683
Correlated random variables      217
Correlation      215—217 770
Correlation coefficient      215
Correlation coefficient, multiple      241 508
Correlation coefficient, squared multiple      241 508
Correlation, causation vs.      324—329
Correlation, coefficient of      215
Correlation, matrix      235
Correlation, variance-covariance matrix and      234—235
Countable additivity      20
Counting rules      See Combinatorics.
Covariance      209—213
Covariance between random vectors      225—227 769—770
Covariance matrices      225—227 771
Covariance matrices, defined      225
Covariance, defined      209
Covariate      621 629—630
Critical region      340 366
Cumulative hazard function      59
De Morgan's laws      6
Deciles      46
Decision      341 368
Degree of monomial      429
Degree of polynomial      429
Degrees of freedom for chi-squared distribution      344
Degrees of freedom for F distribution      350
Degrees of freedom for t distribution      347
Deletion, stepwise      558
Density function      38—44 761
Density function, conditional      300—307
Density function, defined      38
Density function, estimating unknown      125
Density function, joint      242
Density function, lack of uniqueness      39
Density function, marginal      331
Density function, mode of      137
Density function, multivariate      242—252
Density function, posterior      331
Density function, prior      331
Density function, symmetric about zero      49 95
Density function, unimodal      137
Density-probability function      331
Dependence      209—273
Dependent random variables      70 219
Derivative matrix      252
Design distribution      582—586
Design matrix      444 500
Design of Experiments, The (Fisher)      411
Design points      412
Design points, collinear      441
Design points, coplanar      442
Design probability function      582
Design random variables      582
Design set      412
Design set, symmetric      490
Deviance      742 794
Die      2
DIMENSION      430
Direct sum      579
Dirichlet distribution      251
Dirichlet distribution, density function      251
Discrete distribution      33
Discrete random variable      33 81—87
Discrete random variable, conditional distribution of      278—282
Disjoint sets      6 432
Distribution function      761—762
Distribution function for continuous random variables      46—55
Distribution function for nonnegative, integer-valued random variable      55—58
Distribution function, defined      45
Distribution function, quantiles and      45—46
Distributions      14—23 760—761.
Distributions, Bernouilli      36
Distributions, beta      141—143
Distributions, beta-binomial      337
Distributions, binomial      172—188 768—769
Distributions, Cauchy      51 68
Distributions, chi-square      344—346 774
Distributions, conditional      275
Distributions, continuous      38
distributions, defined      20
Distributions, design      582
Distributions, Dirichlet      251
Distributions, discrete      33
Distributions, exponential      42
Distributions, F      68 349—352 775—776 772—773
Distributions, gamma      135—141 767—768
Distributions, geometric      37
Distributions, hypergeometric      293
Distributions, joint      29
Distributions, logistic      63
Distributions, lognormal      151
Distributions, marginal      331
Distributions, mean vector of      223
Distributions, mixture of      44
Distributions, multinomial      188—194
Distributions, multivariate normal      263—273
Distributions, negative binomial      187 335
Distributions, negative multinomial      194
Distributions, Normal      145—155 766—767
Distributions, Poisson      195—203 769
Distributions, posterior      331
Distributions, prior      331
Distributions, properties of      19—21
Distributions, sample      5—14
Distributions, t      346—349 775
Distributions, uniform      15—18 40
Distributions, Weibull      59
Dose, effective      678
Dose, lethal      678
Dose-response model      676
Double-blind experiment      373
Effect, spurious      326
Effect, true      326
Effective dose      678
Empty set      5
Equality, t test of      375—388 553
Error of approximation      474
Error of prediction      213
Estimate, Bayes'      331
Estimate, best linear unbiased (BLUE)      219
Estimate, bias of      114
Estimate, biased      115
Estimate, consistent      1 ] 5
Estimate, mean squared error of      114—115
Estimate, unbiased      115
Estimate, variance of      115
Estimation      114—116
Event      23
Expectation      81—133 764—765
Expectation, conditional      307—316
Expectation, defined      82
Expectation, multivariate      219—225
Expected value      82 91.
Experiment, compound      9—12
Experiment, double-blind      373
Experiment, factorial      See Factorial experiment.
Experiment, notation and terminology for      411—414
Experiment, screening      590
Experiment, simple      9
Experimental model      419—421 779—781
1 2 3 4
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