An introduction to probability and statistics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2001
|
| Edition: | 2. ed. |
| Series: | Wiley series in probability and statistics : texts and references section
A Wiley interscience publication |
| Subjects: | |
| Online Access: | Publisher description Table of Contents Inhaltsverzeichnis |
| Physical Description: | XV, 716 S. graph. Darst. |
| ISBN: | 0471348465 |
Staff View
MARC
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| 100 | 1 | |a Rohatgi, Vijay K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to probability and statistics |c Vijay K. Rohatgi ; A. K. MD. Ehsanes Saleh |
| 250 | |a 2. ed. | ||
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition xi
Preface to the First Edition xiii
1. Probability 1
1.1 Introduction, 1
1.2 Sample Space, 2
1.3 Probability Axioms, 7
1.4 Combinatorics: Probability on Finite Sample Spaces, 21
1.5 Conditional Probability and Bayes Theorem, 28
1.6 Independence of Events, 33
2. Random Variables and Their Probability Distributions 40
2.1 Introduction, 40
2.2 Random Variables, 40
2.3 Probability Distribution of a Random Variable, 43
2.4 Discrete and Continuous Random Variables, 48
2.5 Functions of a Random Variable, 57
3. Moments and Generating Functions 69
3.1 Introduction, 69
3.2 Moments of a Distribution Function. 69
3.3 Generating Functions, 85
3.4 Some Moment Inequalities, 95
4. Multiple Random Variables 102
4.1 Introduction, 102
vii
viii CONTENTS
4.2 Multiple Random Variables, 102
4.3 Independent Random Variables, 119
4.4 Functions of Several Random Variables, 127
4.5 Covariance, Correlation, and Moments, 149
4.6 Conditional Expectation, 164
4.7 Order Statistics and Their Distributions, 171
5. Some Special Distributions 180
5.1 Introduction, 180
5.2 Some Discrete Distributions, 180
5.3 Some Continuous Distributions, 204
5.4 Bivariate and Multivariate Normal Distributions, 238
5.5 Exponential Family of Distributions, 251
6. Limit Theorems 256
6.1 Introduction, 256
6.2 Modes of Convergence, 256
6.3 Weak Law of Large Numbers, 274
6.4 Strong Law of Large Numbers, 281
6.5 Limiting Moment Generating Functions, 289
6.6 Central Limit Theorem, 293
7. Sample Moments and Their Distributions 306
7.1 Introduction, 306
7.2 Random Sampling, 307
7.3 Sample Characteristics and Their Distributions, 310
7.4 Chi Square, / , and F Distributions: Exact Sampling
Distributions, .324
7.5 Large Sample Theory, 334
7.6 Distribution of(X, S2) in Sampling from a Normal
Population, 339
7.7 Sampling froin a Bivariate Normal Distribution, 344
8. Parametric Point Estimation 353
8.1 Introduction. 353
8.2 Problem of Point Estimation. 354
8.3 Sufficiency. Completeness. and Ancillarity, 358
8.4 Unbiased Estimation, 377
8.5 Unbiased Estimation (Continued): Lower Bound for the Variance
of an Estimator. 391
CONTENTS IX
8.6 Substitution Principle (Method of Moments), 406
8.7 Maximum Likelihood Estimators, 409
8.8 Bayes and Minimax Estimation, 424
8.9 Principle of Equivariance, 442
9. Neyman Pearson Theory of Testing of Hypotheses 454
9.1 Introduction, 454
9.2 Some Fundamental Notions of Hypotheses Testing, 454
9.3 Neyman Pearson Lemma, 464
9.4 Families with Monotone Likelihood Ratio. 472
9.5 Unbiased and Invariant Tests, 479
9.6 Locally Most Powerful Tests, 486
10. Some Further Results of Hypothesis Testing 490
10.1 Introduction, 490
10.2 Generalized Likelihood Ratio Tests, 490
10.3 Chi Square Tests, 500
10.4 t Tests, 512
10.5 F Tests, 518
10.6 Bayes and Minimax Procedures, 520
11. Confidence Estimation 527
11.1 Introduction, 527
11.2 Some Fundamental Notions of Confidence Estimation, 527
11.3 Methods of Finding Confidence Intervals. 532
11.4 Shortest Length Confidence Intervals. 546
1 1.5 Unbiased and Equivariant Confidence Intervals. 553
12. General Linear Hypothesis 561
12.1 Introduction. 561
12.2 General Linear Hypothesis. 561
12.3 Regression Model. 569
12.4 One Way Analysis of Variance. 577
I 2.5 Two Way Analysis of Variance with One Observation per
Cell. 583
I 2.6 Two Way Analysis of Variance with Interaction. 590
13. Nonparametric Statistical Inference 598
13.1 Introduction, 598
X CONTENTS
13.2 (/ Statistics, 598
13.3 Some Single Sample Problems, 608
13.4 Some Two Sample Problems, 624
13.5 Tests of Independence, 633
13.6 Some Applications of Order Statistics, 644
13.7 Robustness, 650
References 663
Frequently Used Symbols and Abbreviations 669
Statistical Tables 673
Answers to Selected Problems 693
Author Index 705
Subject Index 707
|
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| dewey-full | 519.221 519.2 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Technik Mathematik |
| edition | 2. ed. |
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| isbn | 0471348465 |
| language | English |
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| spelling | Rohatgi, Vijay K. Verfasser aut An introduction to probability and statistics Vijay K. Rohatgi ; A. K. MD. Ehsanes Saleh 2. ed. New York [u.a.] Wiley 2001 XV, 716 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics : texts and references section A Wiley interscience publication Stochastik - Lehrbuch Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Statistik (DE-588)4056995-0 s 1\p DE-604 Saleh, A. K. Md. Ehsanes Verfasser aut http://www.loc.gov/catdir/description/wiley0310/00026288.html Publisher description http://www.loc.gov/catdir/toc/onix06/00026288.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504374&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 |
| spellingShingle | Rohatgi, Vijay K. Saleh, A. K. Md. Ehsanes An introduction to probability and statistics Stochastik - Lehrbuch Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4079013-7 (DE-588)4056995-0 |
| title | An introduction to probability and statistics |
| title_auth | An introduction to probability and statistics |
| title_exact_search | An introduction to probability and statistics |
| title_full | An introduction to probability and statistics Vijay K. Rohatgi ; A. K. MD. Ehsanes Saleh |
| title_fullStr | An introduction to probability and statistics Vijay K. Rohatgi ; A. K. MD. Ehsanes Saleh |
| title_full_unstemmed | An introduction to probability and statistics Vijay K. Rohatgi ; A. K. MD. Ehsanes Saleh |
| title_short | An introduction to probability and statistics |
| title_sort | an introduction to probability and statistics |
| topic | Stochastik - Lehrbuch Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Stochastik - Lehrbuch Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie Statistik |
| url | http://www.loc.gov/catdir/description/wiley0310/00026288.html http://www.loc.gov/catdir/toc/onix06/00026288.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009504374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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