Statistical theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York (u.a.)
MacMillan (u.a.)
1976
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 614 S. graph. Darst. |
| ISBN: | 0023708301 |
Staff View
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| 245 | 1 | 0 | |a Statistical theory |c Bernard William Lindgren* |
| 250 | |a 3. ed. | ||
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Record in the Search Index
| _version_ | 1804116450710913024 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
CHAPTER 1 PROBABILITY MODELS 7 1.1 SAMPLE SPACES 2 1.1.1 ELEMENTARY
OUTCOMES 2 1.1.2 COMPOSITION OF EXPERIMENTS 4
7.7.3 EVENTS 8 7.7.4 COMPLEMENTS, INTERSECTIONS, AND UNIONS 11 1.1.5
FUNCTIONS ON A SAMPLE SPACE 16 * 7.7.6 BORE/FIELDS 19
1.2 PROBABILITY 22
7.2.7 PROBABILITY AXIOMS 24 7.2.2 77?E ADDITION LAW 27 *7.2.3
PROBABILITY AND BORE/ SETS 28 7.2.4 7V?E DISCRETE CASE 29
7.2.5 4 P/7OAV MODELS FOR FINITE SPACES 31 7.2.6 NONDISCRETE CASES 32
1.3 DEPENDENCE AND INDEPENDENCE 35
7.3.7 CONDITIONAL PROBABILITY 37 7.3.2 FIAYES THEOREM 41 7.3.3
INDEPENDENT EVENTS 44 7.3.4 INDEPENDENT EXPERIMENTS 46
CHAPTER2 RANDOM VARIABLES AND THEIR
DISTRIBUTIONS 50
2.1 RANDOM VARIABLES AND VECTORS 50 2.1.1 THE DISTRIBUTION FUNCTION 53
*2.7.2 MEASURABILITY 57 2.7 .3 DISCRETE RANDOM VARIABLES 62
2.7.4 CONTINUOUS RANDOM VARIABLES 64 2.7.5 SPECIFICATION OF A
DISTRIBUTION BY ITS C.D.F. 71 2.7.6 FUNCTIONS OF RANDOM VARIABLES 74
2.7.7 BIVARIATE DISTRIBUTIONS 79
2.7.S CONDITIONAL DISTRIBUTIONS 89 2.7.9 INDEPENDENCE 95 2.7.70
MU/TIVARIATE DISTRIBUTIONS 99
VII
IMAGE 2
2.2 EXPECTATION 104
2.2.1 SIMPLE RANDOM VARIABLES 105 2.2.2 EXPECTATION: DISCRETE AND
CONTINUOUS VARIABLES 108 2.2.3 EXPECTATION OF A FUNCTION OF RANDOM
VARIABLES 113 2.2.4 RIEMANN-STIELTJES INTEGRALS 118 +2.2.5 GENERAL
DEFINITION OF EXPECTATION 122
2.3 MOMENTS OF A DISTRIBUTION 126
2.3.1 THE VARIANCE 128 2.3.2 CHEBYSHEV AND RELATED INEQUALITIES 131
2.3.3 COVARIANCE AND CORRELATION 134 2.3.4 VARIANCE OF A SUM 137
2.4 GENERATING FUNCTIONS 141
2.4.1 MOMENT GENERATING FUNCTIONS 142 2.4.2 THE FACTORIAL MOMENT
GENERATING FUNCTION 145 2.4.3 PROBABILITY GENERATING FUNCTIONS 146 2.4.4
THE CHARACTERISTIC FUNCTION 148 2.4.5 MU/TIVARIATE GENERATING FUNCTIONS
151
2.5 LIMIT THEOREMS 153
2.5.1 LAWS OF LARGE NUMBERS 155 2.5.2 THE CENTRAL LIMIT THEOREM 157
CHAPTER3 SOME PARAMETRIC FAMILIES OF DISTRIBUTIONS 161
3.1 DISTRIBUTIONS FOR BERNOULLI TRIALS 161 3.1.1 THE BINOMIAL
DISTRIBUTION 163 3.1.2 THE NEGATIVE BINOMIAL DISTRIBUTION 164 3.1.3
SAMPLING WITHOUT REPLACEMENT 168 3.1.4 APPROXIMATE BINOMIAL
PROBABILITIES (MODERATE P) 173
3.2 THE POISSON PROCESS 775
3.2.1 THE POISSON RANDOM VARIABLE 177 3.2.2 EXPONENTIAL AND GAMMA
DISTRIBUTIONS 181 3.2.3 APPROXIMATING BINOMIAL PROBABILITIES (SMALL P)
182
3.3 THE NORMAL AND RELATED DISTRIBUTIONS 187
3.3.1 THE GENERAL NORMAL DISTRIBUTION 188 3.3.2 THE LOGNORMAL
DISTRIBUTION 190 3.3.3 RAY/EIGH AND MAXWELL DISTRIBUTIONS 191 3.3.4 THE
CHI-SQUARE DISTRIBUTION 193
IMAGE 3
3.4 THE MULTINOMIAL DISTRIBUTION 195
3.5 THE EXPONENTIAL FAMILY 197
CHAPTER A REDUCTION OF DATA 201
4.1 SAMPLING 207 4.1.1 RANDOM SAMPLING 202 4.1.2 FREQUENCY TABULATIONS
205 4.1.3 THE SAMPLE DISTRIBUTION FUNCTION 207
4.2 STATISTICS 209
4.2.1 STATISTICS BASED ON ORDER 210 4.2.2 SAMPLE MOMENTS 211
4.3 SAMPLING DISTRIBUTIONS 214
4.3.1 DISTRIBUTION OF SAMPLE MOMENTS 215 4.3.2 COMPONENTS OF THE ORDER
STATISTIC 217 4.3.3 THE MIDRANGE AND RANGE 219 4.3.4 SAMPLE PERCENTILES
221 4.3.5 THE MONTE CARLO METHOD 222
4.4 SUFFICIENT STATISTICS 224
4.4.1 STATISTICS AND PARTITIONS 224 4.4.2 DEFINITION OF SUFFICIENCY 226
4.4.3 THE FACTORIZATION CRITERION 231 4.4.4 CONSTRUCTING MINIMAL
SUFFICIENT STATISTICS 234 4.4.5 THE EXPONENTIAL FAMILY 237
4.5 LIKELIHOOD 240
4.5.1 THE LIKELIHOOD PRINCIPLE 241 4.5.2 MAXIMUM LIKELIHOOD 242 4.5.3
MONOTONE LIKELIHOOD RATIO 246 4.5.4 INFORMATION IN A SAMPLE 248
CHAPTER 5 ESTIMATION 253
5.1 CRITERIA FOR ESTIMATORS 253 5.1.1 MEAN SQUARED ERROR 254 5.7.2
CONSISTENCY 257 5.7.3 EFFICIENCY 259
5.1.4 REDUCTION OF VARIANCE 264
IMAGE 4
E.2 DERIVING ESTIMATORS 268
5.2.1 THE METHOD OF MOMENTS 268 5.2.2 MAXIMUM LIKELIHOOD ESTIMATION 269
5.3 INTERVAL ESTIMATES 273
CHAPTER 6 TESTING HYPOTHESES 276
6.1 BASIC CONCEPTS 276 6.1.1 SIMPLE H O VERSUS SIMPLE H A 27 9 6.1.2 THE
POWER FUNCTION 282 6.1.3 TESTS OF SIGNIFICANCE 288 6.1.4 TESTS AND
CONFIDENCE INTERVALS 290
6.1.5 LARGE-SAMPLE TESTS FOR THE MEAN 291 6.1.6 RANDOMIZED TESTS 292
6.2 EVALUATION AND CONSTRUCTION OF TESTS 254
6.2. 1 BEST TESTS OF SIMPLE H O VERSUS SIMPLE HI 296 6.2.2 UNIFORMLY
MOST POWERFUL TESTS 304 6.2.3 LIKELIHOOD RATIO TESTS 307
6.3 SEQUENTIAL TESTS 310
6.3.1 THE SEQUENTIAL LIKELIHOOD RATIO TEST 312 6.3.2 FINITE TERMINATION
OF THE TEST 316 6.3.3 THE OPERATING CHARACTERISTIC 318 6.3.4 REQUIRED
SAMPLE SIZE 320
CHAPTERL UNIVARIATE NORMAL INFERENCE 325
7.1 DISTRIBUTION THEORY 325 7.1.1 GAMMA DISTRIBUTIONS 325 7.1.2 BETA
DISTRIBUTIONS 328 7.1.3 THE CHI-SQUARE DISTRIBUTION 331 7. 1.4 THE
DISTRIBUTION OF X AND S 2 332
7.1.5 F AND T DISTRIBUTIONS 335 7.7.6 NONCENTRAL CHI-SQUARE DISTRIBUTION
337
7.2 ONE-SAMPLE PROBLEMS 335
7.2.7 DISPERSION 339 7.2.2 THE MEAN 343 7.2.3 CONFIDENCE REGIONS FOR
MEAN AND VARIANCE 345
IMAGE 5
7.3 COMPARISONS 347
7.3.1 COMPARING VARIANCES 348 7.3.2 COMPARING MEANS 350 7.3.3 PAIRED
COMPARISON OF MEANS 353
CHAPTERS STATISTICAL DECISION THEORY 357
8.1 PRELIMINARIES 357 8.1.1 CONVEX COMBINATIONS 357 8.1.2 UTILITY 360
8.1.3 PERSONAL PROBABILITY 362
8.2 THE NO-DATA PROBLEM 365
8.2.1 LOSS AND REGRET 365 8.2.2 MIXED ACTIONS 368 8.2.3 THE MINIMAX
PRINCIPLE 369 8.2.4 BAYES ACTIONS 374 8.2.5 ADMISSIBILITY 379
8.3 USING DATA IN DECISIONS 382
8.3.1 THE RISK FUNCTION 382 ~K8.3.2 RANDOMIZED DECISION RULES 390 8.3.3
ESTIMATION AND TESTING AS SPECIAL CASES 393 8.3.4 PROPERTIES OF DECISION
RULES 3 97 I 8.3.5 MONOTONE PROBLEMS AND PROCEDURES 399
8.4 USING BAYES THEOREM 403
8.4.1 THE POSTERIOR DISTRIBUTION 404 8.4.2 SOLVING THE DECISION PROBLEM
406 8.4.3 CONJUGATE FAMILIES 410 8.4.4 ESTIMATION AND TESTING 412
*8.5 SEQUENTIAL PROCEDURES 415
8.5.1 THE BAYES DECISION RULE 417 8.5.2 A SEQUENTIAL BAYES TEST 418
CHAPTER^ ANALYSIS OF CATEGORICAL DATA 423
9.1 GOODNESS OF FIT 423 9.1.1 PEARSON S CHI-SQUARE STATISTIC 424 9.1.2
THE LIKELIHOOD-RATIO TEST 426
IMAGE 6
9.2 THE BERNOULLI MODEL 428
9.3 TWO-WAY CONTINGENCY TABLES 431 9.3.1 INDEPENDENCE AND HOMOGENEITY
432 9.3.2 LARGE-SAMPLE TESTS 438 9.3.3 SMALL-SAMPLE TESTS 440 9.3.4
MEASURES OF ASSOCIATION 441 9.3.5 A LOG LINEAR MODEL 444
9.4 THREE-WAY CLASSIFICATIONS 445
9.4.1 COMPLETE INDEPENDENCE 446 9.4.2 HIGHER-ORDER MODELS 448 9.4.3
SELECTING A MODEL 449
CHAPTER 10 MULTIVARIATE DISTRIBUTIONS 453
10.1 TRANSFORMATIONS 453 10.1.1 BIVARIATE TRANSFORMATIONS 454 10.1.2
MU/TIVARIATE TRANSFORMATIONS 459 10.1.3 THE GENERAL LINEAR
TRANSFORMATION 462
10.2 NORMAL DISTRIBUTIONS 465
10.2.1 BIVARIATE NORMAL DISTRIBUTIONS 465 70.2.2 MU/TIVARIATE NORMAL
DISTRIBUTIONS 471
10.3 CORRELATION AND PREDICTION 475
10.3.1 PREDICTION IN A BIVARIATE MODEL 476 10.3.2 CORRELATION IN THE
BIVARIATE NORMAL CASE 477
CHAPTER NONPARAMETRIC INFERENCE 480
11.1 ORDER STATISTICS AND RELATED DISTRIBUTIONS 480 11.1.1 DISTRIBUTION
OF THE ORDER STATISTIC 481 77.7.2 CONDITIONAL DISTRIBUTION GIVEN THE
ORDER STATISTIC 482 7 7.7.3 THE TRANSFORMATION F(X) 484
11.2 GOODNESS OF FIT 486
11.2.1 THE KOLMOGOROV-SMIRNOV TEST 487 7 7.2.2 OTHER TESTS 491 11.2.3
COMPARISON OF DISTRIBUTIONS 494
11.3 RANDOMNESS 497
11.3.1 RUN TESTS 498 11.3.2 OTHER TESTS FOR RANDOMNESS 501
IMAGE 7
11.4 ONE-SAMPLE LOCATION TESTS 505
11.4.1 THE SIGN TEST 505 77.4.2 THE SIGNED-RANK TEST 508 7 1.4.3
ASYMPTOTIC RELATIVE EFFICIENCY 511 11.4.4 CONFIDENCE INTERVALS 513
11.5 TWO-SAMPLE LOCATION PROBLEMS 515
11.5.1 THE MEDIAN TEST 517 77.5.2 THE WILCOXON-MANN-WHITNEY TEST 518 7
7.5.3 THE FISHER-YATES TEST 521
CHAPTER 12 LINEAR MODELS AND ANALYSIS OF VARIANCE 524
12.1 PARTITIONING CHI-SQUARE 524 12.1.1 COCHRAN S THEOREM 525 *A- 72.7.2
PROOF OF THE THEOREM 526
12.2 REGRESSION 528
12.2.1 LEAST SQUARES 529 72.2.2 ESTIMATION OF THE PARAMETERS 532 72.2.3
TESTING HYPOTHESES 536 72.2.4 TESTING LINEARITY 539 72.2.5 SELECTING A
MODEL 542 12.2.6 DESIGNING THE EXPERIMENT 546 72.2.7 PREDICTION 546
72.2.5 THE BIVARIATE NORMAL MODEL 547 72.2.S A MATRIX FORMULATION 549
12.3 MODELS FOR DESIGNED EXPERIMENTS 551
12.3.1 A SINGLE CLASSIFICATION 551 72.3.2 A RANDOM EFFECTS MODEL 556
72.3.3 TWO- WAY CLASSIFICATIONS 558 12.3.4 OTHER DESIGNS 563 72.3.5 THE
MATRIX FORMULATION 565
REFERENCES 569
APPENDIX TABLES 571
ANSWERS TO PROBLEMS 598
INDEX 609
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:42Z |
| institution | BVB |
| isbn | 0023708301 |
| language | English |
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| publisher | MacMillan (u.a.) |
| record_format | marc |
| spelling | Lindgren, Bernard W. Verfasser aut Statistical theory Bernard William Lindgren* 3. ed. New York (u.a.) MacMillan (u.a.) 1976 XIII, 614 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistiek gtt Statistique mathématique Theorieën gtt Statistik Mathematical statistics Theorie (DE-588)4059787-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s Theorie (DE-588)4059787-8 s 1\p DE-604 2\p DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001306444&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lindgren, Bernard W. Statistical theory Statistiek gtt Statistique mathématique Theorieën gtt Statistik Mathematical statistics Theorie (DE-588)4059787-8 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4059787-8 (DE-588)4056995-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Statistical theory |
| title_auth | Statistical theory |
| title_exact_search | Statistical theory |
| title_full | Statistical theory Bernard William Lindgren* |
| title_fullStr | Statistical theory Bernard William Lindgren* |
| title_full_unstemmed | Statistical theory Bernard William Lindgren* |
| title_short | Statistical theory |
| title_sort | statistical theory |
| topic | Statistiek gtt Statistique mathématique Theorieën gtt Statistik Mathematical statistics Theorie (DE-588)4059787-8 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistiek Statistique mathématique Theorieën Statistik Mathematical statistics Theorie Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001306444&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lindgrenbernardw statisticaltheory |