Page 674 - Probability and Statistical Inference

Index 651

257 Accuracy measures 452-455,
Applications 259-263, 543-555 569-571
565-567 Approximate 542
Sample mean 258 Binomial 548-550, 556-558,
Sample variance 262 563
Central moments 77; see also Correlation coefficient 563
Moment of a distribution Poisson 553-554, 559-560, 566
Existence 77-79, 85, 93 Variance stabilizing transforma-
Moment problem 87-88 tions 555-563
Non-existence 77-79
Chi-square distribution 44; see also Confidence coefficient 442
Gamma distribution Interpretation 451-452
Asymptotic property 264 Contrast with credible interval 492-
Density 42, 44 493
Moment generating function Coverage probability 441
(mgf) 85-86 Distribution-free approximate
Moments 76-77, 85-86 Comparing means 544
Reproductive property 192 Estimation of mean 543
Statistical table 626-627 Fixed-width 571-574, 584-587
Combinations; see Counting rules Inversion of a test 444
Complete statistic 318-320 Joint confidence intervals 451, 468-
Basu’s Theorem 324 469, 471, 473, 475
Exponential family 322 Lower 441, 469
Minimal sufficiency 320-323 Multiple comparisons 463-469, 475-
Sufficiency 320-323
Complete sufficient statistic; see 476
Complete statistic One-sample problem 441, 444-446,
Compound distribution 113-115 448-451
Concave function 152-156 Paired difference t 459
Jensen’s inequality 154 Pivotal approach 446-447
Conditional distribution 102-103, Sample size determination 569, 573-
106, 108-109, 115-119, 479 574, 586-588
Conditional expectation 109, 129, Behrens-Fisher problem 579,
487 586
Conditional inference 317-318 Simultaneous confidence
Ancillarity 309-311 intervals; see Joint confidence
Recovery of information 312- intervals
313, 316 Two-sample problem
Conditional probability 9 Comparing locations 457-458
Bayes’s Theorem 14, 15, 53, Comparing means 456, 476
478-479
Independence of events 10, 11, 53 Comparing scales 461-462, 476
Conditional variance 109, 112 Comparing variances 460, 476
Confidence coefficient 442 Two-stage procedure 573-574
Interpretation 451-452 Behrens-Fisher problem 586
Joint confidence 451, 468-469, One sample problem 573
471, 473, 475 Uniform distribution 448, 462
Multiple comparisons 463-469 Upper 441, 469
Confidence interval 441, 569 Using for tests of hypotheses