Introduction to mathematical statistics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Macmillan [u.a.]
1978
|
| Edition: | 4. ed. |
| Series: | Collier MacMillan international editions
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 438 S. |
| ISBN: | 0023557109 0029789907 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Introduction to mathematical statistics
Autor: Hogg, Robert V
Jahr: 1978
Contents Chapter 1 Distributions of Random Variables 1 1.1 Introduction 1 1.2 Algebra of Sets 4 1.3 Set Functions 8 1.4 The Probability Set Function 12 1.5 Random Variables 16 1.6 The Probability Density Function 23 1.7 The Distribution Function 31 1.8 Certain Probability Models 38 1.9 Mathematical Expectation 44 1.10 Some Special Mathematical Expectations 48 1.11 Chebyshev’s Inequality 58 Chapter 2 Conditional Probability and Stochastic Independence 61 2.1 Conditional Probability 61 2.2 Marginal and Conditional Distributions 65 2.3 The Correlation Coefficient 73 2.4 Stochastic Independence 80 Chapter 3 Some Special Distributions 90 3.1 The Binomial, Trinomial, and Multinomial Distributions 90 3.2 The Poisson Distribution 99 3.3 The Gamma and Chi-Square Distributions 103 3.4 The Normal Distribution 109 3.5 The Bivariate Normal Distribution 117 vii
viii Contents Chapter 4 Distributions of Functions of Random Variables 122 4.1 Sampling Theory 122 4.2 Transformations of Variables of the Discrete Type 128 4.3 Transformations of Variables of the Continuous Type 132 4.4 The t and F Distributions 143 4.5 Extensions of the Change-of-Variable Technique 147 4.6 Distributions of Order Statistics 154 4.7 The Moment-Generating-Function Technique 164 4.8 The Distributions of X and nS 2 ja 2 172 4.9 Expectations of Functions of Random Variables 176 Chapter 5 Limiting Distributions 181 5.1 Limiting Distributions 181 5.2 Stochastic Convergence 186 5.3 Limiting Moment-Generating Functions 188 5.4 The Central Limit Theorem 192 5.5 Some Theorems on Limiting Distributions 196 Chapter 6 Estimation 200 6.1 Point Estimation 200 6.2 Measures of Quality of Estimators 207 6.3 Confidence Intervals for Means 212 6.4 Confidence Intervals for Differences of Means 219 6.5 Confidence Intervals for Variances 222 6.6 Bayesian Estimates 227 Chapter 7 Statistical Hypotheses 235 7.1 Some Examples and Definitions 235 7.2 Certain Best Tests 242 7.3 Uniformly Most Powerful Tests 251 7.4 Likelihood Ratio Tests 257
Contents ix Chapter 8 Other Statistical Tests 269 8.1 Chi-Square Tests 269 8.2 The Distributions of Certain Quadratic Forms 278 8.3 A Test of the Equality of Several Means 283 8.4 Noncentral x z and Noncentral F 288 8.5 The Analysis of Variance 291 8.6 A Regression Problem 296 8.7 A Test of Stochastic Independence 300 Chapter 9 Nonparametric Methods 304 9.1 Confidence Intervals for Distribution Quantiles 304 9.2 Tolerance Limits for Distributions 307 9.3 The Sign Test 312 9.4 A Test of Wilcoxon 314 9.5 The Equality of Two Distributions 320 9.6 The Mann-Whitney-Wilcoxon Test 326 9.7 Distributions Under Alternative Hypotheses 331 9.8 Linear Rank Statistics 334 Chapter 10 Sufficient Statistics 341 10.1 A Sufficient Statistic for a Parameter 341 10.2 The Rao-Blackwell Theorem 349 10.3 Completeness and Uniqueness 353 10.4 The Exponential Class of Probability Density Functions 357 10.5 Functions of a Parameter 361 10.6 The Case of Several Parameters 364 Chapter 11 Further Topics in Statistical Inference 11.1 The Rao-Cramdr Inequality 370 11.2 The Sequential Probability Ratio Test 374 11.3 Multiple Comparisons 380 11.4 Classification 385 370
X Contents 11.5 Sufficiency, Completeness, and Stochastic Independence 389 11.6 Robust Nonparametric Methods 396 11.7 Robust Estimation 400 Chapter 12 Further Normal Distribution Theory 405 12.1 The Multivariate Normal Distribution 405 12.2 The Distributions of Certain Quadratic Forms 410 12.3 The Independence of Certain Quadratic Forms 414 Appendix A References 421 Appendix B Tables 423 Appendix C Answers to Selected Exercises 429 Index 435
|
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| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
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| indexdate | 2024-07-09T15:51:30Z |
| institution | BVB |
| isbn | 0023557109 0029789907 |
| language | English |
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| physical | X, 438 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Macmillan [u.a.] |
| record_format | marc |
| series2 | Collier MacMillan international editions |
| spelling | Hogg, Robert V. ca. 20. Jh. Verfasser (DE-588)119507951 aut Introduction to mathematical statistics Robert V. Hogg ; Allen T. Craig 4. ed. New York Macmillan [u.a.] 1978 X, 438 S. txt rdacontent n rdamedia nc rdacarrier Collier MacMillan international editions Statistique mathématique Statistik Mathematical statistics Statistics Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s DE-604 Craig, Allen T. 1905-1978 Verfasser (DE-588)172027195 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001856196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hogg, Robert V. ca. 20. Jh Craig, Allen T. 1905-1978 Introduction to mathematical statistics Statistique mathématique Statistik Mathematical statistics Statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4151278-9 |
| title | Introduction to mathematical statistics |
| title_auth | Introduction to mathematical statistics |
| title_exact_search | Introduction to mathematical statistics |
| title_full | Introduction to mathematical statistics Robert V. Hogg ; Allen T. Craig |
| title_fullStr | Introduction to mathematical statistics Robert V. Hogg ; Allen T. Craig |
| title_full_unstemmed | Introduction to mathematical statistics Robert V. Hogg ; Allen T. Craig |
| title_short | Introduction to mathematical statistics |
| title_sort | introduction to mathematical statistics |
| topic | Statistique mathématique Statistik Mathematical statistics Statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistique mathématique Statistik Mathematical statistics Statistics Einführung |
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