Mathematical statistics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Prentice-Hall
1980
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Prentice-Hall international editions
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 548 S. |
| ISBN: | 0135620821 |
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| 264 | 1 | |a London [u.a.] |b Prentice-Hall |c 1980 | |
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Datensatz im Suchindex
| _version_ | 1804135903953682432 |
|---|---|
| adam_text | PREFACE
INTRODUCTION
/1.1 Historical Background 1
1.2 Mathematical Preliminary: Combinatorial Methods 2
1.3 Mathematical Preliminary: Binomial Coefficients 13
PROBABILITY
^ ^ 2.1 Introduction 24
^^^ 2.2 Sample Spaces 25
^•^ 2.3 Events 28
2.4 The Probability of an Event 35
2.5 Some Rules of Probability 39
2.6 Conditional Probability 49
2.7 Independent Events 55
2.8 Bayes Theorem 59
vi Contents
PROBABILITY DISTRIBUTIONS
f^ 3.1 Random Variables 70
_ ^ 3.2 Discrete Probability Distributions 73
^ ^ 3.3 Continuous Random Variables 84
3.4 Probability Density Functions 85
3.5 Multivariate Distributions 98
3.6 Marginal Distributions 112
3.7 Conditional Distributions 116
MATHEMATICAL EXPECTATION
^ 4.1 Introduction 127
/¦ 4.2 The Expected Value of a Random Variable 128
jR 4.3 Moments 137
4.4 Chebyshev s Theorem 141
4.5 Moment Generating Functions 144
4.6 Product Moments 151
4.7 Moments of Linear Combinations of Random Variables 156
4.8 Conditional Expectations 159
SPECIAL PROBABILITY DISTRIBUTIONS
5 5.1 Introduction 164
5.2 777e Discrete Uniform Distribution 164
5.3 The Bernoulli Distribution 165
5.4 777e Binomial Distribution 166
5.5 The Negative Binomial and Geometric Distributions 175
5.6 The Hypergeometric Distribution 178
5.7 The Poisson Distribution 181
5.8 77?e Multinomial Distribution 189
5.9 The Multivariate Hypergeometric Distribution 191
SPECIAL PROBABILITY DENSITIES
«6.1 Introduction 194
6.2 The Uniform Density 194
6.3 777e Gamma, Exponential, and Chi square Distributions 195
6.4 77?e Beta Distribution 200
6.5 7?7e Normal Distribution 206
Contents vli
6.6 The Normal Approximation to the Binomial Distribution 212
6.7 The Bivariate Normal Distribution 216
FUNCTIONS OF RANDOM VARIABLES
pBH 7.1 Introduction 225
^f 7.2 Distribution Function Technique 226
w 7.3 Transformation of Variable Technique 230
7.4 Moment Generating Function Technique 248
SAMPLING DISTRIBUTIONS
»8.1 Introduction 253
8.2 The Distribution of the Mean 255
8.3 777e Distribution of the Mean: Finite Populations 260
8.4 77?e Chi square Distribution 266
8.5 777e t Distribution 270
8.6 77je F Distribution 273
8.7 Crater Statistics 279
DECISION THEORY
9 9.1 Introduction 286
9.2 7/je Theory of Games 288
9.3 Statistical Games 299
9.4 Decision Criteria 303
9.5 777e Minimax Criterion 303
9.6 77?e fiayes Criterion 305
POINT ESTIMATION
Tf^± 10 1 Introduction 310
Mmm 10 2 Point Estimation 310
MLW W 10.3 Unbiased Estimators 311
10.4 Consistent Estimators 316
10.5 Sufficient Estimators 318
10.6 The Method of Moments 325
10.7 The Method of Maximum Likelihood 327
10.8 Bayesian Estimators 333
viii Contents
INTERVAL ESTIMATION
«11.1 Introduction 341
11.2 Confidence Intervals for Means 342
11.3 Confidence Intervals for Differences Between Means 346
11.4 Confidence Intervals for Proportions 352
11.5 Confidence Intervals for Differences Between Proportions 354
11.6 Confidence Intervals for Variances 356
11.7 Confidence Intervals for Ratios of Two Variances 357
HYPOTHESIS TESTING: THEORY
W f~M 12.1 Statistical Hypotheses 361
M ^^£ 12 2 Testing a Statistical Hypothesis 363
B.^^ 12.3 Losses and Risks 366
12.4 The Neyman Pearson Lemma 367
12.5 The Power Function of a Test 373
12.6 Likelihood Ratio Tests 377
HYPOTHESIS TESTING: APPLICATIONS
WfM 13.1 Introduction 387
Mm~m 13.2 Tests Concerning Means 390
RM_W 13.3 Tests Concerning Differences Between Means 393
13.4 Tests Concerning Variances 399
13.5 Tests Concerning Proportions 403
13.6 Tests Concerning Differences Among k Proportions 406
13.7 Contingency Tables 411
13.8 Goodness of Fit 413
REGRESSION AND CORRELATION
M14.1 Regression 419
14.2 Linear Regression 423
14.3 The Method of Least Squares 425
14.4 Normal Regression Analysis 436
14.5 Normal Correlation Analysis 440
Contents ix
ANALYSIS OF VARIANCE
~W IU0 15.1 Introduction 452
M^^k 15.2 One Way Analysis of Variance 452
MM^F 15.3 Experimental Design 461
15.4 Two Way Analysis of Variance 463
15.5 Some Further Considerations 472
NONPARAMETRIC METHODS
~WM~ 16.1 Introduction 474
ffim 16.2 The Sign Test Alb
MLW F ^ 16.3 The Signed Rank Test 478
16.4 Rank Sum Tests: The U 7esf 480
16.5 Rank Sum Tests: The H Tesf 484
16.6 Tests Sasetf on fluns 488
16.7 77?e ffan/r Correlation Coefficient 492
APPENDIX: THE ALGEBRA OF EVENTS
^J~ 1.1 Boolean Algebra 500
APPENDIX: SUMS AND PRODUCTS
TM~TM~ H 1 Rules for Sums and Products 504
UU 11.2 Special Sums 506
STATISTICAL TABLES 508
ANSWERS TO ODD NUMBERED EXERCISES 528
INDEX 543
|
| adam_txt |
PREFACE
INTRODUCTION
/1.1 Historical Background 1
1.2 Mathematical Preliminary: Combinatorial Methods 2
1.3 Mathematical Preliminary: Binomial Coefficients 13
PROBABILITY
^"^ 2.1 Introduction 24
^^^ 2.2 Sample Spaces 25
^•^ 2.3 Events 28
2.4 The Probability of an Event 35
2.5 Some Rules of Probability 39
2.6 Conditional Probability 49
2.7 Independent Events 55
2.8 Bayes' Theorem 59
vi Contents
PROBABILITY DISTRIBUTIONS
f^ 3.1 Random Variables 70
_"^ 3.2 Discrete Probability Distributions 73
^ ^ 3.3 Continuous Random Variables 84
3.4 Probability Density Functions 85
3.5 Multivariate Distributions 98
3.6 Marginal Distributions 112
3.7 Conditional Distributions 116
MATHEMATICAL EXPECTATION
^ 4.1 Introduction 127
/¦ 4.2 The Expected Value of a Random Variable 128
jR 4.3 Moments 137
4.4 Chebyshev's Theorem 141
4.5 Moment Generating Functions 144
4.6 Product Moments 151
4.7 Moments of Linear Combinations of Random Variables 156
4.8 Conditional Expectations 159
SPECIAL PROBABILITY DISTRIBUTIONS
5 5.1 Introduction 164
5.2 777e Discrete Uniform Distribution 164
5.3 The Bernoulli Distribution 165
5.4 777e Binomial Distribution 166
5.5 The Negative Binomial and Geometric Distributions 175
5.6 The Hypergeometric Distribution 178
5.7 The Poisson Distribution 181
5.8 77?e Multinomial Distribution 189
5.9 The Multivariate Hypergeometric Distribution 191
SPECIAL PROBABILITY DENSITIES
«6.1 Introduction 194
6.2 The Uniform Density 194
6.3 777e Gamma, Exponential, and Chi square Distributions 195
6.4 77?e Beta Distribution 200
6.5 7?7e Normal Distribution 206
Contents vli
6.6 The Normal Approximation to the Binomial Distribution 212
6.7 The Bivariate Normal Distribution 216
FUNCTIONS OF RANDOM VARIABLES
pBH 7.1 Introduction 225
^f 7.2 Distribution Function Technique 226
w 7.3 Transformation of Variable Technique 230
7.4 Moment Generating Function Technique 248
SAMPLING DISTRIBUTIONS
»8.1 Introduction 253
8.2 The Distribution of the Mean 255
8.3 777e Distribution of the Mean: Finite Populations 260
8.4 77?e Chi square Distribution 266
8.5 777e t Distribution 270
8.6 77je F Distribution 273
8.7 Crater Statistics 279
DECISION THEORY
9 9.1 Introduction 286
9.2 7/je Theory of Games 288
9.3 Statistical Games 299
9.4 Decision Criteria 303
9.5 777e Minimax Criterion 303
9.6 77?e fiayes Criterion 305
POINT ESTIMATION
Tf^± 10 1 Introduction 310
Mmm 10 2 Point Estimation 310
MLW W 10.3 Unbiased Estimators 311
10.4 Consistent Estimators 316
10.5 Sufficient Estimators 318
10.6 The Method of Moments 325
10.7 The Method of Maximum Likelihood 327
10.8 Bayesian Estimators 333
viii Contents
INTERVAL ESTIMATION
«11.1 Introduction 341
11.2 Confidence Intervals for Means 342
11.3 Confidence Intervals for Differences Between Means 346
11.4 Confidence Intervals for Proportions 352
11.5 Confidence Intervals for Differences Between Proportions 354
11.6 Confidence Intervals for Variances 356
11.7 Confidence Intervals for Ratios of Two Variances 357
HYPOTHESIS TESTING: THEORY
W f~M 12.1 Statistical Hypotheses 361
M ^^£ 12 2 Testing a Statistical Hypothesis 363
B.^^' 12.3 Losses and Risks 366
12.4 The Neyman Pearson Lemma 367
12.5 The Power Function of a Test 373
12.6 Likelihood Ratio Tests 377
HYPOTHESIS TESTING: APPLICATIONS
WfM 13.1 Introduction 387
Mm~m 13.2 Tests Concerning Means 390
RM_W 13.3 Tests Concerning Differences Between Means 393
13.4 Tests Concerning Variances 399
13.5 Tests Concerning Proportions 403
13.6 Tests Concerning Differences Among k Proportions 406
13.7 Contingency Tables 411
13.8 Goodness of Fit 413
REGRESSION AND CORRELATION
M14.1 Regression 419
14.2 Linear Regression 423
14.3 The Method of Least Squares 425
14.4 Normal Regression Analysis 436
14.5 Normal Correlation Analysis 440
Contents ix
ANALYSIS OF VARIANCE
~W IU0 15.1 Introduction 452
M^^k 15.2 One Way Analysis of Variance 452
MM^F 15.3 Experimental Design 461
15.4 Two Way Analysis of Variance 463
15.5 Some Further Considerations 472
NONPARAMETRIC METHODS
~WM~ 16.1 Introduction 474
ffim 16.2 The Sign Test Alb
MLW F ^ 16.3 The Signed Rank Test 478
16.4 Rank Sum Tests: The U 7esf 480
16.5 Rank Sum Tests: The H Tesf 484
16.6 Tests Sasetf on fluns 488
16.7 77?e ffan/r Correlation Coefficient 492
APPENDIX: THE ALGEBRA OF EVENTS
^J~ 1.1 Boolean Algebra 500
APPENDIX: SUMS AND PRODUCTS
TM~TM~ H 1 Rules for Sums and Products 504
UU 11.2 Special Sums 506
STATISTICAL TABLES 508
ANSWERS TO ODD NUMBERED EXERCISES 528
INDEX 543 |
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| author | Freund, John E. 1921-2004 Walpole, Ronald E. |
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| author_facet | Freund, John E. 1921-2004 Walpole, Ronald E. |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
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| spelling | Freund, John E. 1921-2004 Verfasser (DE-588)123809797 aut Mathematical statistics John E. Freund ; Ronald E. Walpole 3. ed. London [u.a.] Prentice-Hall 1980 548 S. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall international editions Mathematical statistics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 3\p DE-604 Walpole, Ronald E. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015157823&sequence=000002&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Freund, John E. 1921-2004 Walpole, Ronald E. Mathematical statistics Mathematical statistics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4056995-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| title | Mathematical statistics |
| title_auth | Mathematical statistics |
| title_exact_search | Mathematical statistics |
| title_exact_search_txtP | Mathematical statistics |
| title_full | Mathematical statistics John E. Freund ; Ronald E. Walpole |
| title_fullStr | Mathematical statistics John E. Freund ; Ronald E. Walpole |
| title_full_unstemmed | Mathematical statistics John E. Freund ; Ronald E. Walpole |
| title_short | Mathematical statistics |
| title_sort | mathematical statistics |
| topic | Mathematical statistics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical statistics Wahrscheinlichkeitstheorie Statistik Einführung Lehrbuch |
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