Stochastics :: introduction to probability and statistics /
This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. It is addressed to students with an interest in the mathematical side of stochastics. Stochastic concepts, models and metho...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English German |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
©2012.
|
| Ausgabe: | 2nd rev., extended ed. |
| Schriftenreihe: | De Gruyter textbook.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. It is addressed to students with an interest in the mathematical side of stochastics. Stochastic concepts, models and methods are motivated by examples and developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems offer applications and supplements to the text. |
| Beschreibung: | 1 online resource (ix, 407 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 391-394) and index. |
| ISBN: | 3110293609 9783110293609 |
Internformat
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| 100 | 1 | |a Georgii, Hans-Otto. | |
| 240 | 1 | 0 | |a Stochastik. |l English |
| 245 | 1 | 0 | |a Stochastics : |b introduction to probability and statistics / |c Hans-Otto Georgii ; translated by Marcel Ortgiese, Ellen Baake and the Author. |
| 250 | |a 2nd rev., extended ed. | ||
| 260 | |a Berlin ; |a Boston : |b De Gruyter, |c ©2012. | ||
| 300 | |a 1 online resource (ix, 407 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Textbook | |
| 504 | |a Includes bibliographical references (pages 391-394) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; Mathematics and Chance; I Probability Theory; 1 Principles of Modelling Chance; 1.1 Probability Spaces; 1.2 Properties and Construction of Probability Measures; 1.3 Random Variables; Problems; 2 Stochastic Standard Models; 2.1 The Uniform Distributions; 2.2 Urn Models with Replacement; 2.3 Urn Models without Replacement; 2.4 The Poisson Distribution; 2.5 Waiting Time Distributions; 2.6 The Normal Distributions; Problems; 3 Conditional Probabilities and Independence; 3.1 Conditional Probabilities; 3.2 Multi-Stage Models; 3.3 Independence. | |
| 505 | 8 | |a 3.4 Existence of Independent Random Variables, Product Measures3.5 The Poisson Process; 3.6 Simulation Methods; 3.7 Tail Events; Problems; 4 Expectation and Variance; 4.1 The Expectation; 4.2 Waiting Time Paradox and Fair Price of an Option; 4.3 Variance and Covariance; 4.4 Generating Functions; Problems; 5 The Law of Large Numbers and the Central Limit Theorem; 5.1 The Law of Large Numbers; 5.2 Normal Approximation of Binomial Distributions; 5.3 The Central Limit Theorem; 5.4 Normal versus Poisson Approximation; Problems; 6 Markov Chains; 6.1 The Markov Property; 6.2 Absorption Probabilities. | |
| 505 | 8 | |a 6.3 Asymptotic Stationarity6.4 Recurrence; Problems; II Statistics; 7 Estimation; 7.1 The Approach of Statistics; 7.2 Facing the Choice; 7.3 The Maximum Likelihood Principle; 7.4 Bias and Mean Squared Error; 7.5 Best Estimators; 7.6 Consistent Estimators; 7.7 Bayes Estimators; Problems; 8 Confidence Regions; 8.1 Definition and Construction; 8.2 Confidence Intervals in the Binomial Model; 8.3 Order Intervals; Problems; 9 Around the Normal Distributions; 9.1 The Multivariate Normal Distributions; 9.2 The X2-, F- and t-Distributions; Problems; 10 Hypothesis Testing; 10.1 Decision Problems. | |
| 505 | 8 | |a 10.2 Neyman-Pearson Tests10.3 Most Powerful One-Sided Tests; 10.4 Parameter Tests in the Gaussian Product Model; Problems; 11 Asymptotic Tests and Rank Tests; 11.1 Normal Approximation of Multinomial Distributions; 11.2 The Chi-Square Test of Goodness of Fit; 11.3 The Chi-Square Test of Independence; 11.4 Order and Rank Tests; Problems; 12 Regression Models and Analysis of Variance; 12.1 Simple Linear Regression; 12.2 The Linear Model; 12.3 The Gaussian Linear Model; 12.4 Analysis of Variance; Problems; Solutions; Tables; References; List of Notation; Index. | |
| 520 | |a This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. It is addressed to students with an interest in the mathematical side of stochastics. Stochastic concepts, models and methods are motivated by examples and developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems offer applications and supplements to the text. | ||
| 650 | 0 | |a Probabilities |v Textbooks. | |
| 650 | 0 | |a Stochastic processes |v Textbooks. | |
| 650 | 0 | |a Mathematical statistics |v Textbooks. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
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| 650 | 7 | |a Probabilities |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
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Datensatz im Suchindex
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|---|---|
| _version_ | 1816882221102923776 |
| adam_text | |
| any_adam_object | |
| author | Georgii, Hans-Otto |
| author_facet | Georgii, Hans-Otto |
| author_role | |
| author_sort | Georgii, Hans-Otto |
| author_variant | h o g hog |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273 .G45613 2012 |
| callnumber-search | QA273 .G45613 2012 |
| callnumber-sort | QA 3273 G45613 42012 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 440 |
| collection | ZDB-4-EBA |
| contents | Preface; Mathematics and Chance; I Probability Theory; 1 Principles of Modelling Chance; 1.1 Probability Spaces; 1.2 Properties and Construction of Probability Measures; 1.3 Random Variables; Problems; 2 Stochastic Standard Models; 2.1 The Uniform Distributions; 2.2 Urn Models with Replacement; 2.3 Urn Models without Replacement; 2.4 The Poisson Distribution; 2.5 Waiting Time Distributions; 2.6 The Normal Distributions; Problems; 3 Conditional Probabilities and Independence; 3.1 Conditional Probabilities; 3.2 Multi-Stage Models; 3.3 Independence. 3.4 Existence of Independent Random Variables, Product Measures3.5 The Poisson Process; 3.6 Simulation Methods; 3.7 Tail Events; Problems; 4 Expectation and Variance; 4.1 The Expectation; 4.2 Waiting Time Paradox and Fair Price of an Option; 4.3 Variance and Covariance; 4.4 Generating Functions; Problems; 5 The Law of Large Numbers and the Central Limit Theorem; 5.1 The Law of Large Numbers; 5.2 Normal Approximation of Binomial Distributions; 5.3 The Central Limit Theorem; 5.4 Normal versus Poisson Approximation; Problems; 6 Markov Chains; 6.1 The Markov Property; 6.2 Absorption Probabilities. 6.3 Asymptotic Stationarity6.4 Recurrence; Problems; II Statistics; 7 Estimation; 7.1 The Approach of Statistics; 7.2 Facing the Choice; 7.3 The Maximum Likelihood Principle; 7.4 Bias and Mean Squared Error; 7.5 Best Estimators; 7.6 Consistent Estimators; 7.7 Bayes Estimators; Problems; 8 Confidence Regions; 8.1 Definition and Construction; 8.2 Confidence Intervals in the Binomial Model; 8.3 Order Intervals; Problems; 9 Around the Normal Distributions; 9.1 The Multivariate Normal Distributions; 9.2 The X2-, F- and t-Distributions; Problems; 10 Hypothesis Testing; 10.1 Decision Problems. 10.2 Neyman-Pearson Tests10.3 Most Powerful One-Sided Tests; 10.4 Parameter Tests in the Gaussian Product Model; Problems; 11 Asymptotic Tests and Rank Tests; 11.1 Normal Approximation of Multinomial Distributions; 11.2 The Chi-Square Test of Goodness of Fit; 11.3 The Chi-Square Test of Independence; 11.4 Order and Rank Tests; Problems; 12 Regression Models and Analysis of Variance; 12.1 Simple Linear Regression; 12.2 The Linear Model; 12.3 The Gaussian Linear Model; 12.4 Analysis of Variance; Problems; Solutions; Tables; References; List of Notation; Index. |
| ctrlnum | (OCoLC)826685195 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2nd rev., extended ed. |
| format | Electronic eBook |
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| genre | Textbooks fast |
| genre_facet | Textbooks |
| id | ZDB-4-EBA-ocn826685195 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:10Z |
| institution | BVB |
| isbn | 3110293609 9783110293609 |
| language | English German |
| lccn | 2012024232 |
| oclc_num | 826685195 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (ix, 407 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter textbook. |
| series2 | De Gruyter Textbook |
| spelling | Georgii, Hans-Otto. Stochastik. English Stochastics : introduction to probability and statistics / Hans-Otto Georgii ; translated by Marcel Ortgiese, Ellen Baake and the Author. 2nd rev., extended ed. Berlin ; Boston : De Gruyter, ©2012. 1 online resource (ix, 407 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Textbook Includes bibliographical references (pages 391-394) and index. Print version record. Preface; Mathematics and Chance; I Probability Theory; 1 Principles of Modelling Chance; 1.1 Probability Spaces; 1.2 Properties and Construction of Probability Measures; 1.3 Random Variables; Problems; 2 Stochastic Standard Models; 2.1 The Uniform Distributions; 2.2 Urn Models with Replacement; 2.3 Urn Models without Replacement; 2.4 The Poisson Distribution; 2.5 Waiting Time Distributions; 2.6 The Normal Distributions; Problems; 3 Conditional Probabilities and Independence; 3.1 Conditional Probabilities; 3.2 Multi-Stage Models; 3.3 Independence. 3.4 Existence of Independent Random Variables, Product Measures3.5 The Poisson Process; 3.6 Simulation Methods; 3.7 Tail Events; Problems; 4 Expectation and Variance; 4.1 The Expectation; 4.2 Waiting Time Paradox and Fair Price of an Option; 4.3 Variance and Covariance; 4.4 Generating Functions; Problems; 5 The Law of Large Numbers and the Central Limit Theorem; 5.1 The Law of Large Numbers; 5.2 Normal Approximation of Binomial Distributions; 5.3 The Central Limit Theorem; 5.4 Normal versus Poisson Approximation; Problems; 6 Markov Chains; 6.1 The Markov Property; 6.2 Absorption Probabilities. 6.3 Asymptotic Stationarity6.4 Recurrence; Problems; II Statistics; 7 Estimation; 7.1 The Approach of Statistics; 7.2 Facing the Choice; 7.3 The Maximum Likelihood Principle; 7.4 Bias and Mean Squared Error; 7.5 Best Estimators; 7.6 Consistent Estimators; 7.7 Bayes Estimators; Problems; 8 Confidence Regions; 8.1 Definition and Construction; 8.2 Confidence Intervals in the Binomial Model; 8.3 Order Intervals; Problems; 9 Around the Normal Distributions; 9.1 The Multivariate Normal Distributions; 9.2 The X2-, F- and t-Distributions; Problems; 10 Hypothesis Testing; 10.1 Decision Problems. 10.2 Neyman-Pearson Tests10.3 Most Powerful One-Sided Tests; 10.4 Parameter Tests in the Gaussian Product Model; Problems; 11 Asymptotic Tests and Rank Tests; 11.1 Normal Approximation of Multinomial Distributions; 11.2 The Chi-Square Test of Goodness of Fit; 11.3 The Chi-Square Test of Independence; 11.4 Order and Rank Tests; Problems; 12 Regression Models and Analysis of Variance; 12.1 Simple Linear Regression; 12.2 The Linear Model; 12.3 The Gaussian Linear Model; 12.4 Analysis of Variance; Problems; Solutions; Tables; References; List of Notation; Index. This second revised and extended edition presents the fundamental ideas and results of both, probability theory and statistics, and comprises the material of a one-year course. It is addressed to students with an interest in the mathematical side of stochastics. Stochastic concepts, models and methods are motivated by examples and developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems offer applications and supplements to the text. Probabilities Textbooks. Stochastic processes Textbooks. Mathematical statistics Textbooks. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Mathematical statistics fast Probabilities fast Stochastic processes fast Textbooks fast Print version: 9783110292541 3110292548 (DLC) 2012024232 De Gruyter textbook. http://id.loc.gov/authorities/names/n94049545 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=530592 Volltext |
| spellingShingle | Georgii, Hans-Otto Stochastics : introduction to probability and statistics / De Gruyter textbook. Preface; Mathematics and Chance; I Probability Theory; 1 Principles of Modelling Chance; 1.1 Probability Spaces; 1.2 Properties and Construction of Probability Measures; 1.3 Random Variables; Problems; 2 Stochastic Standard Models; 2.1 The Uniform Distributions; 2.2 Urn Models with Replacement; 2.3 Urn Models without Replacement; 2.4 The Poisson Distribution; 2.5 Waiting Time Distributions; 2.6 The Normal Distributions; Problems; 3 Conditional Probabilities and Independence; 3.1 Conditional Probabilities; 3.2 Multi-Stage Models; 3.3 Independence. 3.4 Existence of Independent Random Variables, Product Measures3.5 The Poisson Process; 3.6 Simulation Methods; 3.7 Tail Events; Problems; 4 Expectation and Variance; 4.1 The Expectation; 4.2 Waiting Time Paradox and Fair Price of an Option; 4.3 Variance and Covariance; 4.4 Generating Functions; Problems; 5 The Law of Large Numbers and the Central Limit Theorem; 5.1 The Law of Large Numbers; 5.2 Normal Approximation of Binomial Distributions; 5.3 The Central Limit Theorem; 5.4 Normal versus Poisson Approximation; Problems; 6 Markov Chains; 6.1 The Markov Property; 6.2 Absorption Probabilities. 6.3 Asymptotic Stationarity6.4 Recurrence; Problems; II Statistics; 7 Estimation; 7.1 The Approach of Statistics; 7.2 Facing the Choice; 7.3 The Maximum Likelihood Principle; 7.4 Bias and Mean Squared Error; 7.5 Best Estimators; 7.6 Consistent Estimators; 7.7 Bayes Estimators; Problems; 8 Confidence Regions; 8.1 Definition and Construction; 8.2 Confidence Intervals in the Binomial Model; 8.3 Order Intervals; Problems; 9 Around the Normal Distributions; 9.1 The Multivariate Normal Distributions; 9.2 The X2-, F- and t-Distributions; Problems; 10 Hypothesis Testing; 10.1 Decision Problems. 10.2 Neyman-Pearson Tests10.3 Most Powerful One-Sided Tests; 10.4 Parameter Tests in the Gaussian Product Model; Problems; 11 Asymptotic Tests and Rank Tests; 11.1 Normal Approximation of Multinomial Distributions; 11.2 The Chi-Square Test of Goodness of Fit; 11.3 The Chi-Square Test of Independence; 11.4 Order and Rank Tests; Problems; 12 Regression Models and Analysis of Variance; 12.1 Simple Linear Regression; 12.2 The Linear Model; 12.3 The Gaussian Linear Model; 12.4 Analysis of Variance; Problems; Solutions; Tables; References; List of Notation; Index. Probabilities Textbooks. Stochastic processes Textbooks. Mathematical statistics Textbooks. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Mathematical statistics fast Probabilities fast Stochastic processes fast |
| title | Stochastics : introduction to probability and statistics / |
| title_alt | Stochastik. |
| 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 ; translated by Marcel Ortgiese, Ellen Baake and the Author. |
| title_fullStr | Stochastics : introduction to probability and statistics / Hans-Otto Georgii ; translated by Marcel Ortgiese, Ellen Baake and the Author. |
| title_full_unstemmed | Stochastics : introduction to probability and statistics / Hans-Otto Georgii ; translated by Marcel Ortgiese, Ellen Baake and the Author. |
| title_short | Stochastics : |
| title_sort | stochastics introduction to probability and statistics |
| title_sub | introduction to probability and statistics / |
| topic | Probabilities Textbooks. Stochastic processes Textbooks. Mathematical statistics Textbooks. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Mathematical statistics fast Probabilities fast Stochastic processes fast |
| topic_facet | Probabilities Textbooks. Stochastic processes Textbooks. Mathematical statistics Textbooks. MATHEMATICS Probability & Statistics Stochastic Processes. Mathematical statistics Probabilities Stochastic processes Textbooks |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=530592 |
| work_keys_str_mv | AT georgiihansotto stochastik AT georgiihansotto stochasticsintroductiontoprobabilityandstatistics |