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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Alemán |
| Publicado: |
Berlin ; Boston :
De Gruyter,
Ã2012.
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| Edición: | 2nd rev., extended ed. |
| Colección: | De Gruyter textbook.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.