Stochastics: Introduction to Probability and StatisticsWalter de Gruyter, 27.08.2008 - 379 Seiten This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically. |
Inhalt
7 | |
26 | |
3 Conditional Probabilities and Independence | 50 |
4 Expectation and Variance | 90 |
5 The Law of Large Numbers and the Central Limit Theorem | 117 |
6 Markov Chains | 149 |
7 Estimation | 187 |
8 Confidence Regions | 222 |
9 Around the Normal Distributions | 241 |
10 Hypothesis Testing | 255 |
11 Asymptotic Tests and Rank Tests | 283 |
12 Regression Models and Analysis of Variance | 318 |
Backmatter
| 349 |
Häufige Begriffe und Wortgruppen
alternative arbitrary assumption asymptotic balls Bernoulli sequence beta distribution binomial distribution called central limit theorem confidence confidence interval consider convergence in distribution Corollary corresponding countable defined definition depend determine distributed with parameter distribution density distribution function equation error level Example exists expectation Figure find finite first gamma distribution Gaussian product model Hence implies independent random variables inequality large numbers law of large Lebesgue density lemma likelihood function likelihood ratio linear Markov chain maximum likelihood estimator means multinomial distribution n-fold null hypothesis null hypothesis H0 observations obtain outcomes Poisson distributions Poisson process probability measure probability space Proof properties quantiles real random variable regression rejection region Remark sample space standard normal distribution statistical model stochastic Suppose test problem transition matrix unbiased estimator uniform distribution uniformly variance