Page 672 - Probability and Statistical Inference

Index

A Chi-square distribution to
normal distribution 264
Analysis of variance 200 F distribution to Chi-square
Helmert transformation for distribution 265, 267-270
normal distribution 197-199, Poisson distribution to normal
236, 325, 336 distribution 553-554, 559-560
Independent unit splitting of Student’s t distribution to
sample variance 200 normal distribution 264-267
Ancillarity 309-311 Tail comparison with
Conditional inference 317-318 normal distribution 46-47
Location family 314-316 Asymptotic distribution; see
Location-scale family 314-316 Approximate distribution
Pivotal approach 446 Axioms of probability 6-7
Confidence interval 446-447
Recovery of information 312- B
313, 316
Scale family 314-316 Bahadur efficiency 567
Ancillary statistic; see Ancillarity Basu’s Theorem 324
Approximate confidence interval Applications 325-327, 337-338
542 Complete sufficiency 320-323
Binomial distribution Bayes estimator 478, 485-487
One-sample case 548-549 Bayesian methods 477
Two-sample case 549-550 Bayes point estimate 485-487
Variance stabilizing Bayes risk 486
transformation 556-557 Bayesian risk 486
Correlation coefficient Frequentist risk 485-486
Variance stabilizing Bayes test 493-494
transformation 562-563 Credible intervals 478
Distribution-free Contrast with confidence
One-sample case 543-544 intervals 492-493
Two-sample case 544-545 Credible sets 488
Poisson distribution Highest posterior density
One-sample case 553 489-492
Two-sample case 553-554 Posterior distribution 479-480
Variance stabilizing Prior distribution 479
transformation 559-560 Conjugate prior 481-484
Approximation of distributions Inverse gamma 498-500
Binomial distribution to normal Non-conjugate prior
distribution 277, 548-549, 556- 494-497, 504-505
557 Pareto distribution 502-503
Binomial distribution to Poisson Test 493-494
distribution 34-35 Bayes’s Theorem 14
649