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in ANOVA, 573, 577, 600, 614 and, 198 vs. f test, 576 |
F test and, 589, 593, 600, 604 Weibull distribution and, 203 two-factor, 587, 593, 600 |
in mixed effects model, 593, 604 Exponential random variable(s) type I error in, 574 |
in random effects model, 580, Box~Muller transformation Full quadratic model, 695 |
593-594 and, 271 |
in regression, 681 cdf of, 199 G |
Expected value expected value of, 198 Galton—Watson branching process, |
conditional, 255 independence of, 242 281 |
of a continuous random mean of, 198 Gamma distribution |
variable, 171 in order statistics, 272, 275 chi-squared distribution and, 200 |
covariance and, 247 pdf of, 198 definition of, 195 |
of a discrete random variable, 112 transformation of, 220, 267, 270 density function for, 195 |
of a function, 115, 245-246 variance of, 198 Erlang distribution and, 201 |
heavy-tailed distribution and, Exponential regression model, 721 estimators of parameters, 351, |
114-115, 120 Exponential smoothing, 48 355, 358 |
of jointly distributed random Extreme outliers, 3941 exponential distribution and, |
variables, 245 Extreme value distribution, 217 198-200 |
Law of Large Numbers and, 303 Poisson distribution and, 783 |
of a linear combination, 306 F standard, 195 |
of mean squares (see Expected _Factorial notation, 69 Weibull distribution and, 203 |
mean squares) Factorization theorem, 363 Gamma function |
moment generating function Factors, 552 incomplete, 196, 217 |
and, 122, 175 Failure rate function, 230 properties of, 195 |
moments and, 121 Family of probability distributions, Gamma random variables, 195 |
in order statistics, 272-273, 277 104, 213 Geometric distribution, 143, 225 |
of sample mean, 277, 296 F distribution Geometric random variables, 143 |
of sample standard deviation, chi-squared distribution and, 323. Goodness-of-fit test |
340, 379 definition of, 323 for composite hypotheses, |
of sample total, 296 expected value of, 325 732, 741 |
of sample variance, 339 for model utility test, 649, 687, 709 definition of, 723 |
Experiment noncentral, 574-575 for homogeneity, 745-747 |
binomial, 128, 240, 724 pdf of, 324 for independence, 747-749 |
definition of, 52 Finite population correction factor, 141 simple, 724-730 |
double-blind, 523 Fisher information, 371 Grand mean, 555, 584 |
--- Trang 852 --- |
Index 839 |
H Intersection of events model utility test and, 721 |
Half-normal plot, 220 definition of, 53 in Neyman-Pearson theorem, 470 |
Histogram multiplication rule for probability significance level and, 470, 471 |
bimodal, 18 of, 77-79 sufficiency and, 380 |
class intervals in, 15-17 Invariance principle, 357 tests, 475 |
construction of, 12-20 Inverse matrix, 712 Limiting relative frequency, 58, 59 |
density, 17-18 Linear combination |
multimodal, 19 J distribution of, 309 |
Pareto diagram, 24 Jacobian, 267 expected value of, 306 |
for pmf, 103 Jensen’s inequality, 231 independence in, 306 |
symmetric, 19 Joint cumulative distribution variance of, 307 |
unimodal, 18 function, 282 Linear probabilistic model, 617, 627 |
Hodges-Lehmann estimator, 379 Jointly distributed random variables Linear regression |
Homogeneity, 745~747 bivariate normal distribution additive model for, 614, 682, 705 |
Hyperexponential distribution, 229 of, 258-260 ANOVA in, 649, 699, 768 |
Hypergeometric distribution, conditional distribution of, confidence intervals in, 643, 656 |
138-141 253-263 correlation coefficient in, |
and binomial distribution, 141 correlation coefficients for, 249 662-671 |
Hypergeometric random variable, covariance between, 248 definition of, 617 |
138-141 expected value of function of, degrees of freedom in, 631, |
Hypothesis 245-246 685, 708 |
alternative, 426 independence of, 238-239 least squares estimates in, |
composite, 732-741, 744 linear combination of, 306-312 625-636, 679 |
definition of, 426 in order statistics, 274-276 likelihood ratio test in, 721 |
errors in testing of, 428-434 pdf of (see Joint probability mies in, 631, 639 |
notation for, 426 density functions) model utility test in, 648, 687, 708 |
null, 426 pmf of (sce Joint probability mass parameters in, 617, 624-636, 682 |
research, 427 functions) percentage of explained variation |
simple, 469 transformation of, 265-270 in, 633-634 |
Hypothetical population, 6 variance of function of, 252, 307 prediction interval in, 654, 658, 689 |
Joint marginal density function, 245 residuals in, 629, 674, 685 |
I Joint probability mass function, summary statistics in, 627 |
Inclusive inequalities, 136 233-234 sums of squares in, 631-636, 686 |
Incomplete beta function, 207 Joint probability table, 233 ratio in, 648, 669, 690 |
Incomplete gamma function, Line graph, 102-103 |
196-197, 217 K Location parameter, 217, 367 |
Independence K-out-of-n system, 153 Logistic distribution, 279 |
chi-squared test for, 749 Kruskal-Wallis test, 784-785 Logistic regression model |
conditional distribution and, K-tuple, 68-69 contingency tables for, 749-751 |
257-258 definition of, 620-622 |
correlation coefficient L fit of, 650-651 |
and, 250 lag 1 autocorrelation coefficient, 674 mes in, 650 |
covariance and, 250, 252 Laplace distribution, 478 in multiple regression analysis, 699 |
of events, 84-88 Laplace’s rule of succession, 782 Logit function, 621, 650 |
of jointly distributed random Largest extreme value distribution, 228 Lognormal distribution, 205-205, 233 |
variables, 238-239, 241 Law of Large Numbers, 303-304, Lognormal random variables, 205-206 |
in linear combinations, 306-307 322-323, 376 |
mutual, 87 Law of total probability, 79 M |
pairwise, 90, 94 Least squares estimates, 626, 645, Mann-Whitney test, 766-770 |
in simple random sample, 287 679, 683-684 Marginal distribution, 234, 236, 253 |
Independent variable, 614 Level « test, 433 Marginal probability density |
Indicator variables, 696 Level of a factor, 552, 583, 593 functions, 236 |
Inductive reasoning, 6 Levene test, 562-563 Marginal probability mass |
Inferential statistics, 5-6 Leverages, 714715 functions, 234 |
Inflection point, 180 Likelihood function, 354, 470,475 Matrices in regression analysis, |
Intensity function, 156 Likelihood ratio 705-715 |
Interaction, 597-602, 603-606, chi-squared statistic for, 477 Maximum likelihood estimator |
693-698 definition of, 470 for Bernoulli parameter, 377 |
Intercept, 214, 617, 627 mle and, 475 for binomial parameter, 377 |
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