Mathematical statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Prentice-Hall
1972
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 463 S. |
| ISBN: | 0135622492 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1
INTRODUCTION, 1
1.1 Historical Background, 1
1.2 Mathematical Preliminary: Sets, 2
1.5.1 Discrete sample spaces, 5
1.2.2 Subsets and events, 7
1.2.8 Operations on sets, 8
1.24 The algebra of sets, 10
1.2.5 Set functions, 13
1.3 Mathematical Preliminary: Combinatorial Methods, 17
1.3.1 Tree diagrams, 18
1.3.2 Permutations, 21
l.3.3 Combinations, 24
1.3.4 Binomial coefficients, 25
2
PROBABILITY, 36
2.1 Introduction, 36
2.2 The Mathematics of Probability, 37
2.2.1 The postulates of probability, 38
2.2.2 Some elementary theorems, 41
2.2.3 Further addition rules, 43
2.3 Conditional Probability, 50
2.3.1 Multiplication rules, 54
2.3.2 Independent events, 55
2.3.3 Bayes rule, 57
vii
viii CONTENTS
3
PROBABILITY FUNCTIONS, 68
3.1 Random Variables, 68
3.2 Probability Functions, 70
3.3 Special Probability Distributions, 73
3.3.1 The discrete uniform distribution, 73
3.3.2 The Bernoulli distribution, 73
3.3.3 The binomial distribution, 74
3.3.4 The hypergeometric distribution, 77
3.3.5 The geometric distribution, 79
3.3.6 The negative binomial distribution, 80
3.3.7 The Poisson distribution, 81
3.4 Multivariate Distributions, 90
3.4.1 The multinomial distribution, 95
4
PROBABILITY DENSITIES, 101
4.1 The Continuous Case, 101
4.2 Probability Densities, 102
4.3 Special Probability Densities, 110
4.3.1 The uniform distribution, 111
4.3.2 The exponential distribution, 111
4.3.3 The gamma distribution, 112
4.3.4 The beta distribution, 114
4 3.5 The normal distribution, 115
4.4 Change of Variable, 119
4.5 Multivariate Probability Densities, 129
4 5.1 Joint marginal distributions, 132
4 5.2 Conditional probability densities, 133
5
MATHEMATICAL EXPECTATION, 141
5.1 Introduction, 141
5.2 Moments, 146
5.2.1 Chebyshev s theorem, 149
5.2.2 Moment generating functions, 151
CONTENTS ix
5.3 Moments of Special Probability Distributions, 155
5.S.I Moments of the binomial distribution, 156
5.3.2 Moments of the hypergeometric distribution, 159
5.3.3 Moments of the Poisson distribution, 160
5.3.4 Moments of the gamma distribution, 162
5.3.5 Moments of the beta distribution, 163
5.3.6 Moments of the normal distribution, 164
5.4 Moment Generating Functions and Limiting Distributions, 174
5.5 Product Moments, 178
6
SUMS OF RANDOM VARIABLES, 182
6.1 Sums of Random Variables, 182
6.1.1 Sums of random variables: convolutions, 184
6.1.2 Sums of random variables: moment generating functions, 191
6.2 Moments of Linear Combinations of Random Variables, 195
6.2.1 The distribution of the mean, 197
6.2.8 Differences between means and differences
between proportions, 199
6.2.3 The distribution of the mean: finite populations, 203
6.3 The Central Limit Theorem, 206
7
SAMPLING DISTRIBUTIONS, 210
7.1 Introduction, 210
7.2 Sampling From Normal Populations, 210
7.2.1 The distribution of x, 211
7.2.2 The chi square distribution and the distribution o/s2, 212
7.2.3 The F distribution, 218
7.24 The t distribution, 220
7.3 Sampling Distributions of Order Statistics, 224
8
DECISION THEORY, 231
8.1 Introduction, 231
8.2 The Theory of Games, 233
8.3 Statistical Games, 243
X CONTENTS
8.4 Decision Criteria, 247
8.4.1 The minimax criterion, 247
8.4.2 The Bayes criterion, 249
9
ESTIMATION, 254
9.1 Introduction, 254
9.2 Point Estimation, 254
9.3 Properties of Estimators, 255
9.5.1 Unbiased estimators, 256
9.8.2 Relative efficiency, 259
9.3.3 Consistent estimators, 260
9.3.4 Sufficient estimators, 262
9.4 Methods of Point Estimation, 266
9.4.1 The method of moments, 266
9.4.2 The method of maximum likelihood, 267
9.5 Confidence Intervals, 271
9.5.1 Confidence intervals for means, 274
9.5.2 Confidence intervals for proportions, 275
9.5.8 Confidence intervals for variances, 276
9.6 Bayesian Estimation, 280
9.6.1 Estimation of the binomial parameter 8, 281
9.6.2 Estimation of the mean of a normal population, 282
10
HYPOTHESIS TESTING: THEORY, 289
10.1 Introduction, 289
10.2 Simple Hypotheses, 290
10.2.1 Losses, errors, and risks, 291
10.2.2 The Neyman Pearson lemma, 293
10.3 Composite Hypotheses, 299
10.8.1 The power function of a test, 299
10.3.2 Likelihood ratio tests, 304
11
HYPOTHESIS TESTING: APPLICATIONS, 314
11.1 Introduction, 314
11.2 Tests Concerning Means, 315
11.2.1 Tests concerning one mean, 316
11.2.2 Differences between means, 318
CONTENTS xi
11.3 Tests Concerning Variances, 324
11.4 Tests Based on Count Data, 327
11.4.1 Tests concerning proportions, 328
11.4.2 Differences among k proportions, 329
H.4.8 Contingency tables, 334
II.4.4 Goodness of fit, 337
12
HYPOTHESIS TESTING: NONPARAMETRIC METHODS, 343
12.1 Introduction, 343
12.2 The Sign Test, 343
12.3 The Median Test, 344
12.4 Tests Based on Bank Sums, 347
12.5 Tests Based on Buns, 352
12.5.1 Runs above and below the median, 354
13
REGRESSION AND CORRELATION, 358
13.1 Begression, 358
13.1.1 Linear regression, 361
15.1.2 The method of least squares, 363
13.2 The Bivariate Normal Distribution, 372
18.2.1 Normal correlation analysis, 378
18.2.2 Normal regression analysis, 382
14
ANALYSIS OF VARIANCE, 393
14.1 Experimental Design, 393
14.2 One Way Analysis of Variance, 395
14.3 Two Way Analysis of Variance, 404
14.8.1 Two way analysis without interaction, 405
14.3.2 Two way analysis with interaction, 409
14.4 Some Further Considerations, 416
xii CONTENTS
APPENDIX: SUMS AND PRODUCTS, 419
A.I Rules for Sums and Products, 419
A.2 Some Special Sums, 420
STATISTICAL TABLES, 423
ANSWERS TO ODD NUMBERED EXERCISES, 446
INDEX, 457
|
| adam_txt |
CONTENTS
1
INTRODUCTION, 1
1.1 Historical Background, 1
1.2 Mathematical Preliminary: Sets, 2
1.5.1 Discrete sample spaces, 5
1.2.2 Subsets and events, 7
1.2.8 Operations on sets, 8
1.24 The algebra of sets, 10
1.2.5 Set functions, 13
1.3 Mathematical Preliminary: Combinatorial Methods, 17
1.3.1 Tree diagrams, 18
1.3.2 Permutations, 21
l.3.3 Combinations, 24
1.3.4 Binomial coefficients, 25
2
PROBABILITY, 36
2.1 Introduction, 36
2.2 The Mathematics of Probability, 37
2.2.1 The postulates of probability, 38
2.2.2 Some elementary theorems, 41
2.2.3 Further addition rules, 43
2.3 Conditional Probability, 50
2.3.1 Multiplication rules, 54
2.3.2 Independent events, 55
2.3.3 Bayes' rule, 57
vii
viii CONTENTS
3
PROBABILITY FUNCTIONS, 68
3.1 Random Variables, 68
3.2 Probability Functions, 70
3.3 Special Probability Distributions, 73
3.3.1 The discrete uniform distribution, 73
3.3.2 The Bernoulli distribution, 73
3.3.3 The binomial distribution, 74
3.3.4 The hypergeometric distribution, 77
3.3.5 The geometric distribution, 79
3.3.6 The negative binomial distribution, 80
3.3.7 The Poisson distribution, 81
3.4 Multivariate Distributions, 90
3.4.1 The multinomial distribution, 95
4
PROBABILITY DENSITIES, 101
4.1 The Continuous Case, 101
4.2 Probability Densities, 102
4.3 Special Probability Densities, 110
4.3.1 The uniform distribution, 111
4.3.2 The exponential distribution, 111
4.3.3 The gamma distribution, 112
4.3.4 The beta distribution, 114
4 3.5 The normal distribution, 115
4.4 Change of Variable, 119
4.5 Multivariate Probability Densities, 129
4 5.1 Joint marginal distributions, 132
4 5.2 Conditional probability densities, 133
5
MATHEMATICAL EXPECTATION, 141
5.1 Introduction, 141
5.2 Moments, 146
5.2.1 Chebyshev's theorem, 149
5.2.2 Moment generating functions, 151
CONTENTS ix
5.3 Moments of Special Probability Distributions, 155
5.S.I Moments of the binomial distribution, 156
5.3.2 Moments of the hypergeometric distribution, 159
5.3.3 Moments of the Poisson distribution, 160
5.3.4 Moments of the gamma distribution, 162
5.3.5 Moments of the beta distribution, 163
5.3.6 Moments of the normal distribution, 164
5.4 Moment Generating Functions and Limiting Distributions, 174
5.5 Product Moments, 178
6
SUMS OF RANDOM VARIABLES, 182
6.1 Sums of Random Variables, 182
6.1.1 Sums of random variables: convolutions, 184
6.1.2 Sums of random variables: moment generating functions, 191
6.2 Moments of Linear Combinations of Random Variables, 195
6.2.1 The distribution of the mean, 197
6.2.8 Differences between means and differences
between proportions, 199
6.2.3 The distribution of the mean: finite populations, 203
6.3 The Central Limit Theorem, 206
7
SAMPLING DISTRIBUTIONS, 210
7.1 Introduction, 210
7.2 Sampling From Normal Populations, 210
7.2.1 The distribution of x, 211
7.2.2 The chi square distribution and the distribution o/s2, 212
7.2.3 The F distribution, 218
7.24 The t distribution, 220
7.3 Sampling Distributions of Order Statistics, 224
8
DECISION THEORY, 231
8.1 Introduction, 231
8.2 The Theory of Games, 233
8.3 Statistical Games, 243
X CONTENTS
8.4 Decision Criteria, 247
8.4.1 The minimax criterion, 247
8.4.2 The Bayes criterion, 249
9
ESTIMATION, 254
9.1 Introduction, 254
9.2 Point Estimation, 254
9.3 Properties of Estimators, 255
9.5.1 Unbiased estimators, 256
9.8.2 Relative efficiency, 259
9.3.3 Consistent estimators, 260
9.3.4 Sufficient estimators, 262
9.4 Methods of Point Estimation, 266
9.4.1 The method of moments, 266
9.4.2 The method of maximum likelihood, 267
9.5 Confidence Intervals, 271
9.5.1 Confidence intervals for means, 274
9.5.2 Confidence intervals for proportions, 275
9.5.8 Confidence intervals for variances, 276
9.6 Bayesian Estimation, 280
9.6.1 Estimation of the binomial parameter 8, 281
9.6.2 Estimation of the mean of a normal population, 282
10
HYPOTHESIS TESTING: THEORY, 289
10.1 Introduction, 289
10.2 Simple Hypotheses, 290
10.2.1 Losses, errors, and risks, 291
10.2.2 The Neyman Pearson lemma, 293
10.3 Composite Hypotheses, 299
10.8.1 The power function of a test, 299
10.3.2 Likelihood ratio tests, 304
11
HYPOTHESIS TESTING: APPLICATIONS, 314
11.1 Introduction, 314
11.2 Tests Concerning Means, 315
11.2.1 Tests concerning one mean, 316
11.2.2 Differences between means, 318
CONTENTS xi
11.3 Tests Concerning Variances, 324
11.4 Tests Based on Count Data, 327
11.4.1 Tests concerning proportions, 328
11.4.2 Differences among k proportions, 329
H.4.8 Contingency tables, 334
II.4.4 Goodness of fit, 337
12
HYPOTHESIS TESTING: NONPARAMETRIC METHODS, 343
12.1 Introduction, 343
12.2 The Sign Test, 343
12.3 The Median Test, 344
12.4 Tests Based on Bank Sums, 347
12.5 Tests Based on Buns, 352
12.5.1 Runs above and below the median, 354
13
REGRESSION AND CORRELATION, 358
13.1 Begression, 358
13.1.1 Linear regression, 361
15.1.2 The method of least squares, 363
13.2 The Bivariate Normal Distribution, 372
18.2.1 Normal correlation analysis, 378
18.2.2 Normal regression analysis, 382
14
ANALYSIS OF VARIANCE, 393
14.1 Experimental Design, 393
14.2 One Way Analysis of Variance, 395
14.3 Two Way Analysis of Variance, 404
14.8.1 Two way analysis without interaction, 405
14.3.2 Two way analysis with interaction, 409
14.4 Some Further Considerations, 416
xii CONTENTS
APPENDIX: SUMS AND PRODUCTS, 419
A.I Rules for Sums and Products, 419
A.2 Some Special Sums, 420
STATISTICAL TABLES, 423
ANSWERS TO ODD NUMBERED EXERCISES, 446
INDEX, 457 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
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| dewey-sort | 3519.5 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| spelling | Freund, John E. 1921-2004 Verfasser (DE-588)123809797 aut Mathematical statistics John E. Freund 2. ed. London Prentice-Hall 1972 463 S. txt rdacontent n rdamedia nc rdacarrier Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015157822&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 Mathematical statistics Mathematical statistics Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4079013-7 (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 |
| title_fullStr | Mathematical statistics John E. Freund |
| title_full_unstemmed | Mathematical statistics John E. Freund |
| title_short | Mathematical statistics |
| title_sort | mathematical statistics |
| topic | Mathematical statistics Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Mathematical statistics Statistik Wahrscheinlichkeitstheorie Einführung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015157822&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT freundjohne mathematicalstatistics |