Introduction to mathematical statistics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Macmillan
1965
|
| Edition: | 2. ed., 1. pr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 383 S. |
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MARC
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| 100 | 1 | |a Hogg, Robert V. |d ca. 20. Jh. |e Verfasser |0 (DE-588)119507951 |4 aut | |
| 245 | 1 | 0 | |a Introduction to mathematical statistics |c Robert V. Hogg and Allen T. Craig |
| 250 | |a 2. ed., 1. pr. | ||
| 264 | 1 | |a New York, NY |b Macmillan |c 1965 | |
| 300 | |a X, 383 S. | ||
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Record in the Search Index
| _version_ | 1804128274237882368 |
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| adam_text | Contents
Part One • PROBABILITY
Introduction 3
Chapter 1 Elementary Probability Spaces
1. Introduction 5
2. Events 9
3. Law of Total Probability 14
4. Conditional Probability 15
5. Law of Compound Probability 15
6. Independent Events 18
Chapter 2 General Probability Spaces
7. Introduction 21
8. Definition of a Probability Space 22
9. Axioms for 5F 22
10. Axioms for P, and Related Theorems 23
11. Conditional Probability, and the Law of
Compound Probability 26
12. Independence 26
13. Bayes Formula 28
14. Summary 31
Chapter 3 Random Variables
15. Introduction 33
16. Probability Space Induced on the Set of Real
Numbers by a Random Variable 36
17. Graphical Representation of a Discrete
Random Variable 38
18. Physical Representation of a Discrete
Random Variable 41
19. Physical Representation of a Continuous
Random Variable 41
ix
X CONTENTS
20. Graphical Representation of a Continuous
Random Variable *
21. Distribution Function
22. Expectation and Variance °
23. Summary 53
Chapter 4 Multivariate Distributions
24. A Pair of Discrete Random Variables ^
25. Probability Space Induced on Ri by a Pair
of Random Variables 59
26. Joint Distribution of Discrete Random
Variables; General 62
27. Continuous Random Variables
28. Continuous Random Variables;
General 67
29. Conditional Distributions of Discrete
Random Variables 71
30. Independence of Discrete Random Variables 4
* 31. Matrix Condition for Independence of Two
Discrete Random Variables 5
32. Conditional Distributions of Continuous
Random Variables 77
33. Independence of Continuous Random
Variables 81
34. Summary 84
Chapter 5 The Algebra of Expectations
35. Bases for Operations 86
36. Conditional Expectation 92
Part Two • STATISTICS
Introduction 99
Chapter 6 Random Sampling
37. Introduction 101
38. Random Sampling from an Arbitrary
Population 105
39. Combinations 110
40. Summary 111
*41. The Multinomial Distribution 115
* 42. The Poisson Distribution 117
CONTENTS Xi
Chapter 7 The Law of Large Numbers
43. The Sample Mean 126
44. Chebyshev s Inequality 127
45. The Law of Large Numbers 130
Chapter 8 Estimation of Parameters
46. Introduction 136
47. Unbiased Estimators 138
48. Consistent Estimators 140
* 49. Consistency of Sample Moments 141
50. Maximum Likelihood Estimators 143
51. Maximum Likelihood; Continuous
Distribution 145
52. Maximum Likelihood Estimation of the
Variance of a Normal Population 150
* 53. The Method of Moments 151
* 54. Bayes Estimates 153
* 55. Estimation as Decision Making 154
* 56. Efficiency and Sufficiency 155
Chapter 9 Central Limit Theorem
57. Central Limit Theorem 164
* 58. Normal and Poisson Approximations to the
Binomial Distribution 169
* 59. Asymptotically Efficient Estimators 170
Chapter 10 Confidence Intervals and Tests of Hypotheses
60. Confidence Interval for the Mean 174
61. Test of a Hypothesis 175
62. Confidence Intervals for Population Mean.
Testing a Hypothesis on the Sample
Mean 176
63. A General Method for Determining Confi¬
dence Intervals and Testing Hypotheses
of the Form 6 = 0O 177
64. Testing the Difference between Two Means 182
65. Standard Deviations Known 182
66. Standard Deviations Unknown, but Assumed
Equal 183
xii CONTENTS
* Chapter 11 Decision Theory and Bayesian Inference
67. Introduction 188
68. Principles of Choice 191
69. Utility, Loss, and Risk 194
70. Mixed Strategies, Admissible Strategies, and
Complete Classes 196
71. Existence of Utility 197
72. Bayes Principle 198
73. Precise Measurement 203
Chapter 12 Regression
74. Central Problem 208
75. The Correlation Coefficient 210
76. The Regression Curve 212
77. Least Squares Linear Fit of Data 212
78. Regression Line in Sampling from a Bivariate
Population 215
79. Normal Bivariate Population 216
80. Correlation Coefficient in Sampling from
Normal Bivariate Population 220
Chapter 13 Sampling from a Normal Population
81. Moment Generating Function 224
82. The x2 Distribution 230
83. Student s ^ distribution 235
* 84. Proof of the Central Limit Theorem 236
* 85. Normal Regression 240
Chapter 14 Testing Hypotheses
86. Introduction 249
87. Testing a Simple Hypothesis against a Simple
Alternative 250
88. Choice of a Null Hypothesis 254
89. The Power Function 254
90. Testing the Difference between Means from
Normal Populations 258
91. The F Distribution 260
* 92. The Likelihood Ratio Test 261
*93. Most Powerful Tests 264
* 94. Consistent Tests 267
* 95. x2 Tests 274
X2 Tests of Probabilities 276
Testing Goodness of Fit to a Hypothetical
Distribution 276
CONTENTS xj}i
X2 Test for Independence; Contingency
Tables 278
X2 Test for Homogeneity 279
* 96. The Kolmogorov Test for Goodness of Fit 280
* Chapter 15 Experimental Design and Analysis of Variance
97. The Analysis of Variance 286
98. Completely Randomized Design 292
99. Use of a Table of Random Numbers 292
100. Fisher s Lemma 293
101. Two Way Classification; Two Factor
Experiments 296
102. Randomized Block Design 301
103. Latin Squares 301
104. Other Methods 305
* Chapter 16 Other Sampling Methods
105. Sampling from a Finite Group 314
106. Stratified Random Sampling 319
107. Sequential Sampling 325
Termination of the Sequential Procedure 327
Determination of A and B 331
Expected Number of Trials 333
108. Quality Control; Inspection Sampling;
Acceptance Sampling 335
Control Chart 335
Sampling Inspection 336
* Chapter 17 Distribution Free Methods
109. Introduction 345
110. Distribution of F(x) 346
111. Joint Distribution of F(y{), F(y2), • • ¦, F(yn) 347
112. Confidence Intervals for Median and
Percentage Points 348
113. Tolerance Limits 351
114. Runs Test for Randomness 354
115. The Distribution of the Number of Runs 356
116. Runs Test for Identity of Two Distributions 361
117. Kolmogorov Smirnov Test of Identity of
Populations 363
118. Median Test 363
xjv CONTENTS
References 372
Tables
I. Binomial Probability Function 373
II. Summed Binomial Probability Function 377
III. Poisson Probability Function 381
IV. Summed Poisson Probability Function 385
V. Normal Distribution 389
VI. Chi square Distribution 390
VII. Student s Distribution 391
VIII. F Distribution 392
IX. Values of e~x 394
X. Natural Logarithms of Numbers 396
XI. Common Logarithms of Numbers 400
XII. Random Numbers 402
XIII. Kolmogorov s Statistic 407
Index 409
Answers 417
|
| any_adam_object | 1 |
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| author_sort | Hogg, Robert V. ca. 20. Jh |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., 1. pr. |
| format | Book |
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| spelling | Hogg, Robert V. ca. 20. Jh. Verfasser (DE-588)119507951 aut Introduction to mathematical statistics Robert V. Hogg and Allen T. Craig 2. ed., 1. pr. New York, NY Macmillan 1965 X, 383 S. txt rdacontent n rdamedia nc rdacarrier 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 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=009202718&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 Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4151278-9 (DE-588)4123623-3 |
| 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 and Allen T. Craig |
| title_fullStr | Introduction to mathematical statistics Robert V. Hogg and Allen T. Craig |
| title_full_unstemmed | Introduction to mathematical statistics Robert V. Hogg and Allen T. Craig |
| title_short | Introduction to mathematical statistics |
| title_sort | introduction to mathematical statistics |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik Einführung Lehrbuch |
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