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| Ïîèñê ïî óêàçàòåëÿì |
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| Stone C.J.D. — Course in Probability and Statistics |
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| Ïðåäìåòíûé óêàçàòåëü |
Experimental model, canonical regression and 679—681 788—789
Experimental model, defined 419
Experimental region 411
Experimental unit 628
Exponential distribution 42
Exponential distribution, density function 42
Exponential distribution, distribution function 48
Exponential distribution, gamma distribution and 136 137 140
Exponential distribution, mean 88
Exponential distribution, memoryless property 278
Exponential distribution, quantiles 48
Exponential distribution, second moment 99
Exponential distribution, standard deviation 105
Exponential distribution, variance 105
Exponential family 635 662—672 787
Exponential family, canonical parameter 635 663
Exponential family, defined 663
Exponential family, maximum likelihood estimation and 690—691
Exponential family, normalizing function 663
Extrapolation 491
Extrasensory perception (ESP) 186
F distribution 68 349—352 775—776
F distribution, chi-square approximation to 351
F distribution, defined 350
F distribution, density function 350
F distribution, distribution function 350
F distribution, quantiles 350 832
F distribution, t distribution and 351
F statistic 390 570 574 744
F test 388—395 568—578 778—779 784
F test of constancy 573—574
F test of goodness-of-fit 574—575
F test, likelihood-ratio test and 636 744
F test, P-value of 570
F test, t test and 393—394 575—577
Factor 396
Factor-level combination 411
Factorial 134
Factorial experiment 407—415.
Factorial experiment, complete 407 412
Factorial experiment, defined 411
Factorial experiment, fractional 4(2
Factorial experiment, regular fractional 409
Failure time 59 74—75
Fertilizer experiment 411 588—589
Finite-dimensional space 430
First moment 82
Fisher, Ronald A. 411 634
Fitted sum of squares (FSS) 507
Fourth moment 155
frequency 2 9
Frequency, relative 2 10
Gamma distribution 135—141 767—768
Gamma distribution as exponential family 672
Gamma distribution, chi-square distribution as 345
Gamma distribution, defined 136
Gamma distribution, density function 136 204
Gamma distribution, distribution function 136—137
Gamma distribution, mean 137
Gamma distribution, Mode 137—138
Gamma distribution, normal approximation to 156—157
Gamma distribution, Poisson process and 204
Gamma distribution, second moment 137
Gamma distribution, standard deviation 137
Gamma distribution, variance 137
Gamma function 134—135
Gamma function, values at half-integers 143—144
Generalized linear model 681
Generalized linear Models (McCullagh and Nelder) 68!
Geometric distribution 37
Geometric distribution, distribution function 56—57
Geometric distribution, mean 82—83
Geometric distribution, memory less property 277
Geometric distribution, probability function 37
Geometric distribution, quartiles 57—58
Geometric distribution, second moment 104
Geometric distribution, variance 104
Geometric series, sum of 37
Goodness-of-fit test 574 742—745 785
Gradient 640
Gram matrix 455—456 500
Greatest integer 42
Half-integer correction 180—181
Hazard function 59
Heterogeneity 624
Heteroskedastic regression model 419
Homogeneity, test of 388 573
Homoskedastic linear regression model 419
Homoskedastic regression model 419
Homoskedastic regression model, experimental version 420
Hunter, J. Stuart 407 605
Hunter, William G. 407 605
Hyper geometric distribution 292—300
Hyper geometric distribution, defined 293
Hyper geometric distribution, exact P-values and 653
Hyper geometric distribution, mean 294
Hyper geometric distribution, modes 296
Hyper geometric distribution, multivariate 297—299
Hyper geometric distribution, probability function 293 296
Hyper geometric distribution, variance 294
Hyperplane 232—233
Hypothesis, alternative 366
Hypothesis, null 367
Hypothesis, test of 341
Identifiable space 405 438
Identifiable space, orthogonal projection onto 471—479
Identitiability 438—447
Identitiability, defined 438
Incomplete block design 624
Independence 69—80 763—764
Independence, correlation and 217
Independence, defined 70
Independent linear spaces 579
Independent random variables 70
Independent random variables, pairwise 583
Independent random variables, sequences of 77—78
Indeterminate expected value 91
Indicator function 36 432
Indicator random variable 35
Indicator random variable, mean 93
Indicator random variable, variance 101
Inequality, t test of 365—375 553
Infinite expected value 91
Infinite population 289
Infinite-dimensional space 430
Information matrix 723
Inner product 454—460 494
Inner product, defined 455 494
Input vector 415
Input vector, random 422—423 681—682
Input-response model 415—419 779
Input-response model, canonical regression and 675—679 787—788
Input-response model, defined 415
Integration by parts 88
Interaction 571—572 595—610
Interaction component 606
Interaction subspace 599
Interaction term 417 595
Interaction, three-factor 605—608
Interpolating function 400
Interpolating polynomial 403—404 450
Intersection 5—6
Inverse image 30
Inverse-scale parameter 204
Invertible transformation 252—263
Iteratively reweighted least-squares method 709—723
Iteratively reweighted least-squares method, defined 711
Jacobian 252
John, Peter W.M. 396 409
Joint density function 242
| Joint density-probability function 331
Joint distribution 29 76 J 263
Joint probability function 189 283
Lack-of-fit sum of squares (LSS) 424 495 497
Lack-of-fit sum of squares (LSS), deviance and 744
Lagrange interpolation formula 403 450
Latin square 411 588
Law of Averages 113
Law of Large Numbers 110—114
Law of Large Numbers, strong 113
Law of large numbers, weak 113
Law of relative frequencies 12—13 114
Least-squares approximation 474
Least-squares approximation in nonidentifiable space 483
Least-squares estimation 397 423 494—506 781
Least-squares estimation, defined 423
Least-squares fit 397 495
Least-squares linear estimate 397
Least-squares linear fit 397
Least-squares method 396—406 423—425
Least-squares method, defined 397 423
Lethal dose 678
Level 411
Level, allowable 411
Likelihood function 686 688 691
Likelihood ratio 656 737
Likelihood-ratio statistic 737
Likelihood-ratio test 636 656—659 736—737 792
Likelihood-ratio test as goodness-of-fit test 742—743
Likelihood-ratio test, defined 656
Likelihood-ratio test, F test and 636 674 744
Likelihood-ratio test, logistic and Poisson regression and 736—750
Likelihood-ratio test, P-value of 737
Likelihood-ratio test, Wald test and 741—742
Linear canonical regression model 677
linear combination 428
Linear logistic regression model 677
Linear parameter 355 520
Linear parameter, least-squares estimate of 520—521
Linear parameter, nontrivial 356
Linear parameter, trivial 356
Linear Poisson regression model 677
Linear prediction 213—215
Linear prediction, multiple 236—242
Linear regression model 415
Linear regression model, experimental version 419
Linear regression model, homoskedastic 419
Linear regression model, normal 419
Linear regression model, one-sample and multisample models and 421—422
Linear spaces 404 427—433
Linear spaces, defined 429
Linear spaces, identifiability of 438—447
Linear spaces, independent 579
Linear spaces, orthogonal 579
Linear spaces, saturated 448
Linear spaces, sum of 579
Linear spaces, unsaturated 448
Linear transformation 60—65 258 472
Linearly dependent functions 428
Linearly independent functions 428
Link function 664
Location invariant 108
Location parameter 63
Log-likelihood function 687 688 691
Log-odds 53
Logistic distribution 63. See also Standard logistic distribution
Logistic distribution, density function 61
Logistic distribution, distribution function 61
Logistic distribution, quantiles 61
Logistic regression 673—750 794—796
Logistic regression function 675
Logistic regression model 53
Logistic regression model with random input vector 681—682
Logistic regression model, linear 677
logit 53 662
Logit function 53
Lognormal distribution 151
Lower confidence bound 358 522 642
Lube oil experiment 409—410
Lube oil experiment, data 410
Lube oil experiment, interactions and 612—616
Lube oil experiment, quadratic models for 538—550 557—558
Lung cancer study 684 746—747
Lung cancer study, data 684
Main effects 579—595
Main effects, defined 583
Marginal density function 331
Marginal distribution 331
Marginal probability function 331
Markov's inequality 95
Matched pairs 385
Matrices, correlation 234—235
Matrices, covariance 225—227 771
Matrices, variance-covariance 227—234 771—772
Maximum-likelihood equation 700
Maximum-likelihood estimate (MLE) 688
Maximum-likelihood estimate (MLE), existence 701 7
Maximum-likelihood estimate (MLE), normal approximation and 723—736
Maximum-likelihood estimate (MLE), uniqueness 699—701
McCullagh, P. 681
Mean 82 91
Mean rate 205
Mean square 392
Mean squared error (MSE) 114
Mean squared error (MSE) of estimate 114—115
Mean squared error (MSE) of prediction 213—214
Mean vector 223
Mean, second moment and 100
Median 46
Memoryless property of exponential distribution 278
Memoryless property of geometric distribution 277
Mixture of distributions 44
MOD 409
MODE 137
Mode of density function 137
Mode of probability function 176
Moment, first 82
Moment, fourth 155
Moment, second 99
Moment, third 155
Monomial 429
Monotone likelihood-ratio property 672
Monte Carlo method 121
Most powerful test 656
Multinomial distribution 188—194
Multinomial distribution, binomial distribution and 189
Multinomial distribution, covariances 211
Multinomial distribution, defined 190
Multinomial distribution, probability function 189
Multinomial formula 171
Multiple correlation coefficient 241 508
Multiple correlation coefficient, adjusted squared 578
Multiple correlation coefficient, squared 241 508
Multiple linear predication 236—242
Multisample model as linear regression model 421—422 515—516
Multisample model, normal 354—357 776—777
Multivariate density function 242—252 772
Multivariate expectation 219—225 770—771
Multivariate hypergeometric distribution 297—299
Multivariate normal distribution 263—273 772—773
Multivariate normal distribution, conditional distribution 323
Multivariate normal distribution, defined 264
Multivariate normal distribution, density function 264
Multivariate normal distribution, mean vector 264
Multivariate normal distribution, variance-covariance matrix 264
Negative binomial distribution 187 335—336
Negative binomial distribution, mean 336
Negative binomial distribution, probability function 335
Negative binomial distribution, second moment 336
Negative binomial distribution, variance 336
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