Stochastics: Introduction to probability and statistics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2013]
|
| Edition: | 2nd Revised and extended edition |
| Series: | De Gruyter Textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 407 Seiten Illustrationen, Diagramme |
| ISBN: | 9783110292541 9783110293609 3110292548 |
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MARC
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| 100 | 1 | |a Georgii, Hans-Otto |d 1944-2017 |0 (DE-588)10807546X |4 aut | |
| 245 | 1 | 0 | |a Stochastics |b Introduction to probability and statistics |c Hans-Otto Georgii |
| 250 | |a 2nd Revised and extended edition | ||
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2013] | |
| 264 | 4 | |c © 2013 | |
| 300 | |a ix, 407 Seiten |b Illustrationen, Diagramme | ||
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Record in the Search Index
| _version_ | 1805069395206078464 |
|---|---|
| adam_text |
Contents
Preface
v
Mathematics and Chance
1
I Probability Theory
1
Principles of Modelling Chance
7
1.1
Probability Spaces
. 7
1.2
Properties and Construction of Probability Measures
. 14
1.3
Random Variables
. 20
Problems
. 24
2
Stochastic Standard Models
27
2.1
The Uniform Distributions
. 27
2.2
Urn Models with Replacement
. 30
2.3
Urn Models without Replacement
. 35
2.4
The
Poisson
Distribution
. 39
2.5
Waiting Time Distributions
. 40
2.6
The Normal Distributions
. 46
Problems
. 48
3
Conditional Probabilities and Independence
51
3.1
Conditional Probabilities
. 51
3.2
Multi-Stage Models
. 57
3.3
Independence
. 64
3.4
Existence of Independent Random Variables, Product Measures
. 70
3.5
The
Poisson
Process
. 75
3.6
Simulation Methods
. 79
3.7
Tail Events
. 83
Problems
. 86
viii Contents
4
Expectation and Variance
92
4.1
The Expectation
. 92
4.2
Waiting Time Paradox and Fair Price of an Option
. 100
4.3
Variance and Covariance
. 107
4.4
Generating Functions
. 110
Problems
. 114
5
The Law of Large Numbers and the Central Limit Theorem
119
5.1
The Law of Large Numbers
. 119
5.2
Normal Approximation of Binomial Distributions
. 131
5.3
The Central Limit Theorem
. 138
5.4
Normal versus
Poisson
Approximation
. 143
Problems
. 146
6
Markov Chains
151
6.1
The Markov Property
. 151
6.2
Absorption Probabilities
. 155
6.3
Asymptotic Stationarity
. 159
6.4
Recurrence
. 171
Problems
. 181
II Statistics
7
Estimation
191
7.1
The Approach of Statistics
.191
7.2
Facing the Choice
.195
7.3
The Maximum Likelihood Principle
.199
7.4
Bias and Mean Squared Error
.205
7.5
Best Estimators
.207
7.6
Consistent Estimators
.214
7.7
Bayes
Estimators
.218
Problems
.222
8
Confidence Regions
227
8.1
Definition and Construction
.227
8.2
Confidence Intervals in the Binomial Model
. 233
8.3
Order Intervals
.239
Problems
.,.243
Contents
їх
9
Around the Normal Distributions
246
9.1
The Multivariate Normal Distributions
.246
9.2
The
χ2-,
F-
and
t
-Distributions
.249
Problems
.256
10
Hypothesis Testing
260
10.1
Decision Problems
.260
10.2
Neyman-Pearson Tests
.265
10.3
Most Powerful One-Sided Tests
.271
10.4
Parameter Tests in the Gaussian Product Model
.274
Problems
.284
11
Asymptotic Tests and Rank Tests
289
11.1
Normal Approximation of Multinomial Distributions
.289
11.2
The Chi-Square Test of Goodness of Fit
.296
11.3
The Chi-Square Test of Independence
.303
11.4
Order and Rank Tests
.309
Problems
.320
12
Regression Models and Analysis of Variance
325
12.1
Simple Linear Regression
.325
12.2
The Linear Model
.329
12.3
The Gaussian Linear Model
.334
12.4
Analysis of Variance
.342
Problems
.351
Solutions
357
Tables
385
References
391
List of Notation
395
Index
399 |
| any_adam_object | 1 |
| author | Georgii, Hans-Otto 1944-2017 |
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| author_variant | h o g hog |
| building | Verbundindex |
| bvnumber | BV040524549 |
| classification_rvk | QH 440 SK 800 |
| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)820382233 (DE-599)DNB102490623X |
| dewey-full | 519.2 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 519.5 |
| dewey-search | 519.2 519.5 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2nd Revised and extended edition |
| format | Book |
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| institution | BVB |
| isbn | 9783110292541 9783110293609 3110292548 |
| language | English |
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| spelling | Georgii, Hans-Otto 1944-2017 (DE-588)10807546X aut Stochastics Introduction to probability and statistics Hans-Otto Georgii 2nd Revised and extended edition Berlin ; Boston De Gruyter [2013] © 2013 ix, 407 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter Textbook Stochastik (DE-588)4121729-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Stochastik (DE-588)4121729-9 s b DE-604 Erscheint auch als Online-Ausgabe 978-3-11-029360-9 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025370766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Georgii, Hans-Otto 1944-2017 Stochastics Introduction to probability and statistics Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4123623-3 |
| title | Stochastics Introduction to probability and statistics |
| title_auth | Stochastics Introduction to probability and statistics |
| title_exact_search | Stochastics Introduction to probability and statistics |
| title_full | Stochastics Introduction to probability and statistics Hans-Otto Georgii |
| title_fullStr | Stochastics Introduction to probability and statistics Hans-Otto Georgii |
| title_full_unstemmed | Stochastics Introduction to probability and statistics Hans-Otto Georgii |
| title_short | Stochastics |
| title_sort | stochastics introduction to probability and statistics |
| title_sub | Introduction to probability and statistics |
| topic | Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Stochastik Lehrbuch |
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