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840 Index
Maximum likelihood estimator Minimize absolute deviations normal equations in, 683, 685,
(cont.) principle, 477, 679 705-708
Cramér-Rao inequality and, 375. Minimum variance unbiased parameters for, 682
data sufficiency for, 369 estimator, 341-343, 358, and polynomial regression,
Fisher information and, 371, 375 369, 375 691-693
for geometric distribution Mixed effects model, 593~603 prediction interval in, 689
parameter, 742 Mixed exponential distribution, 229 principle of least squares in,
in goodness-of-fit testing, 733 mle. See Maximum likelihood 683-706
in homogeneity test, 745 estimate residuals in, 685, 691, 688, 691,
in independence test, 748 Mode 708, 713
in likelihood ratio tests, 475 of a continuous distribution, squared multiple correlation in,
in linear regression, 631, 639 228, 229 686, 709
in logistic regression, 650 of a data set, 46 sum of squares in, 686, 708-710
sample size and, 357 of a discrete distribution, 156 1 ratios in, 690, 712
score function and, 377 Model utility test, 647-649 Multiplication rule, 77-88
MeNemar’s test, 526, 550 Moment generating function Multiplicative exponential
Mean of a Bernoulli rv, 122, 127 regression model, 721
of Cauchy distribution, 322, of a binomial rv, 135 Multiplicative power regression
342, 761 of a chi-squared rv, 315 model, 721
conditional, 255-257 CLT and, 329-330 Multivariate data, 3, 20
correction for the, 560 of a continuous rv, 175-177 Multivariate hypergeometric
deviations from the, 33, 206, 563, definition of, 122, 175 distribution, 244
631, 739 of a discrete rv, 122-127 Mutually exclusive events, 54, 79
of a function, 115, 245-246 of an exponential rv, 221 MVUE. See Minimum variance
vs. median, 28 of a gamma ry, 195 unbiased estimator
moments about, 121 of a linear combination, 311
outliers and, 27, 28 and moments, 124, 176 N
population, 26 of a negative binomial rv, 143 Negative binomial distribution,
regression to the, 260, 636 of a normal rv, 191 141-144
sample, 25 of a Poisson rv, 149 definition of, 141
of sample total, 296 of a sample mean, 329-330 estimation of parameters, 352, 738
See also Average uniqueness property of, 123,176 Negative binomial random
Mean square Moments variable, 141
expected, 573, 589, 593, 594, definition of, 121 Newton’s binomial theorem, 143
600, 604 method of, 350-352, 358,740 Neyman factorization theorem, 363
lack of fit, 681 and moment generating function, | Neyman-Pearson theorem, 470-475
pure error, 681 124, 176 Noncentrality parameter, 423,
Mean square error Monotonic, 221, 353 574, 582
definition of, 335 Multimodal histogram, 19 Noncentral f distribution, 423
of an estimator, 335 Multinomial distribution, 240,725 Nonhomogeneous Poisson
MVUE and, 341 Multinomial experiment, 240, 724 process, 156
sample size and, 337 Multiple regression Nonstandard normal distribution,
Measurement error, 337 additive model, 682, 705 185-188
Median categorical variables in, 696-699 Normal distribution
in boxplot, 37-38 coefficient of multiple asymptotic, 298, 371, 375, 377
of a distribution, 27, 28 determination, 686, 709 binomial distribution and,
as estimator, 378, 478 confidence intervals in, 712 189-190, 302
vs. mean, 28 covariance matrices in, 711-713 bivariate, 258-260, 310, 318,
outliers and, 26, 28, 29 degrees of freedom in, 685, 477, 677-671
population, 28 696, 708 confidence interval for mean of,
sample, 27, 271 diagnostic plots, 691 383-388, 392, 398, 403
statistic, 378 fitted values in, 685 continuity correction and, 189-190
Mendel’s law of inheritance, 726-728 F ratio in, 687, 709 density curves for, 180
M-estimator, 359, 381 interaction in models for, 693-698 and discrete random variables,
Midfourth, 46 leverages in, 714-715 188-190
Midrange, 333 logistic regression model, 699 goodness-of-fit test for, 730, 740
Mild outlier, 39, 393 in matrix/vector format, 705~715 of linear combination, 309
Minimal sufficient statistic, model utility test in, 687, lognormal distribution and,
366-367, 369 708-709 205, 303
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Index 841
nonstandard, 185-188 estimator for a, 332-346 mean squared error of, 335
pdf for, 179 Fisher information on, 371-377 moments method, 350-352, 358
percentiles for, 182-188, 210 goodness-of-fit tests for, MVUE of, 340-342, 358, 369,
probability plot, 210, 740 728-729, 732-736 375
Ryan—Joiner test for, 747 hypothesis testing for, 427, 450 notation for, 332, 334
standard, 181 location, 217, 367 of a standard deviation and,
1 distribution and, 320-322, 325, maximum likelihood estimate 286, 340
402 of, 354-359, 369 standard error of, 344-346
z table, 181-183 moment estimators for, 350-352 of a variance, 334, 339
Normal equations, 626, 683, 705 MVUE of, 341-343, 358, Point prediction, 405, 628, 684
Normal probability plot, 210, 740 369, 375 Poisson distribution
Normal random variable, 181 noncentrality, 574 Erlang distribution and, 202
Null distribution, 443-444, 760, 780 null value of, 427 expected value, 149, 152
Null hypothesis, 426 of a probability distribution, exponential distribution and, 199
Null set, 54, 57 103-104 gamma distribution and, 783
Null value, 427, 436 in regression, 617-618, 622, goodness-of-fit tests for, 736-738
624-636, 658, 666, 682 in hypothesis testing, 470-472,
o scale, 195, 203, 217-218, 365 474, 482, 550
Observational study, 488 shape, 217-218, 365 mode of, 156
Odds ratio, 621-622, 750-751 sufficient estimation of, 361-369 moment generating function
One-sided confidence interval, Pareto diagram, 24 for, 149
398-399 Pareto distribution, 170, 178, 226 nonhomogeneous, 156
Operating characteristic curve, 137 _ pf. See Probability density function parameter of, 149
Ordered categories, 749-751 Percentiles and Poisson process, 149-151, 199
Ordered pairs, 66-67 for continuous random variables, variance, 149, 152
Order statistics, 271-278, 338, 166-168 Poisson process, 149-151, 194
365-367, 478 in hypothesis testing, 458,740 Polynomial regression model,
sufficiency and, 365-367 in probability plots, 211-216, 740 691-693
Outliers sample, 29, 210-211, 216 Pooled f procedures
in a boxplot, 37-41 of standard normal distribution, and ANOVA, 477, 504-505, 576
definition of, 11 182-184, 211-216 vs. Wilcoxon rank-sum
extreme, 39-41 Permutation, 68, 69, 535-541 procedures, 769
leverage and, 714 Permutation test, 535-541 Posterior probability, 79-81,
mean and, 29, 415-417 PERT analysis, 207 717, 781
median and, 29, 37, 415, 417 Plot Power curves, 574-575
mild, 39 probability, 210-218, 369, 499, Power function of a test, 473-475,