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Stochastics : introduction to probability and statistics

Author: Hans-Otto Georgii
Publisher: Berlin ; New York : Walter De Gruyter, ©2008.
Series: De Gruyter textbook.
Edition/Format:   Book : English : [3rd ed.View all editions and formats
Database:WorldCat
Summary:

Presents the translation of the third edition of the German textbook "Stochastik", which presents the fundamental ideas and results of both probability theory and statistics, and comprises the  Read more...

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Genre/Form: Textbooks
Document Type: Book
All Authors / Contributors: Hans-Otto Georgii
ISBN: 3110191458 9783110191455
OCLC Number: 183147567
Notes: Translated from the third German ed.: Stochastik : Einführung in die Wahrscheinlichkeitstheorie und Statistik, Berlin, Walter de Gruyter, Berlin, 2007.
Description: ix, 370 p. : ill. ; 24 cm.
Contents: aMathematics 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 --
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 --
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 Measures --
3.5. The Poisson Process --
3.6. Simulation Methods --
3.7. Tail Events --
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 --
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 --
6. Markov Chains --
6.1. The Markov Property --
6.2.Absorption Probabilities --
6.3. Asymptotic Stationarity --
6.4. Recurrence --
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 --
8. Confidence Regions --
8.1. Definition and Construction --
8.2. Confidence Intervals in the Binomial Model --
8.3. Order Intervals --
9.Around the Normal Distributions --
9.1. The Multivariate Normal Distributions --
9.2. The X[superscript 2]-, F- and t-Distributions --
10. Hypothesis Testing --
10.1. Decision Problems --
10.2. Neyman-Pearson Tests --
10.3. Most Powerful One-Sided Tests --
10.4. Parameter Tests in the Gaussian Product Model --
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 --
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.
Series Title: De Gruyter textbook.
Other Titles: Stochastik.
Responsibility: Hans-Otto Georgii ; translated by Marcel Ortgiese, Ellen Baake and the author.
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"The book can be used by undergraduate mathematics majors but also by science and engeneering students who wish not only to apply probability and statistics but also to understand how the methods Read more...

 
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