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E-raamat: Stochastics: Introduction to Probability and Statistics 2nd rev. and ext. ed. [De Gruyter e-raamatud]

  • Formaat: 416 pages, 77 Illustrations; 22 Tables, black and white
  • Sari: De Gruyter Textbook
  • Ilmumisaeg: 15-Nov-2012
  • Kirjastus: De Gruyter
  • ISBN-13: 9783110293609
Teised raamatud teemal:
  • De Gruyter e-raamatud
  • Hind: 958,80 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Stochastics: Introduction to Probability and Statistics 2nd rev. and ext. ed.Suurem pilt
  • Formaat: 416 pages, 77 Illustrations; 22 Tables, black and white
  • Sari: De Gruyter Textbook
  • Ilmumisaeg: 15-Nov-2012
  • Kirjastus: De Gruyter
  • ISBN-13: 9783110293609
Teised raamatud teemal:
Wiley OnlineRohkem infot De Gruyter e-raamatute kohta
Raamatu kodulehekülg: http://dx.doi.org/10.1515/9783110293609
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.

Hans-Otto Georgii, Ludwig-Maximilians-Universität Munich, Germany.
Preface v
Mathematics and Chance 1(6)
I Probability Theory
1 Principles of Modelling Chance
7(20)
1.1 Probability Spaces
7(7)
1.2 Properties and Construction of Probability Measures
14(6)
1.3 Random Variables
20(7)
Problems
24(3)
2 Stochastic Standard Models
27(24)
2.1 The Uniform Distributions
27(3)
2.2 Urn Models with Replacement
30(5)
2.3 Urn Models without Replacement
35(4)
2.4 The Poisson Distribution
39(1)
2.5 Waiting Time Distributions
40(6)
2.6 The Normal Distributions
46(5)
Problems
48(3)
3 Conditional Probabilities and Independence
51(41)
3.1 Conditional Probabilities
51(6)
3.2 Multi-Stage Models
57(7)
3.3 Independence
64(6)
3.4 Existence of Independent Random Variables, Product Measures
70(5)
3.5 The Poisson Process
75(4)
3.6 Simulation Methods
79(4)
3.7 Tail Events
83(9)
Problems
86(6)
4 Expectation and Variance
92(27)
4.1 The Expectation
92(8)
4.2 Waiting Time Paradox and Fair Price of an Option
100(7)
4.3 Variance and Covariance
107(3)
4.4 Generating Functions
110(9)
Problems
114(5)
5 The Law of Large Numbers and the Central Limit Theorem
119(32)
5.1 The Law of Large Numbers
119(12)
5.2 Normal Approximation of Binomial Distributions
131(7)
5.3 The Central Limit Theorem
138(5)
5.4 Normal versus Poisson Approximation
143(8)
Problems
146(5)
6 Markov Chains
151(40)
6.1 The Markov Property
151(4)
6.2 Absorption Probabilities
155(4)
6.3 Asymptotic Stationarity
159(12)
6.4 Recurrence
171(20)
Problems
181(10)
II Statistics
7 Estimation
191(36)
7.1 The Approach of Statistics
191(4)
7.2 Facing the Choice
195(4)
7.3 The Maximum Likelihood Principle
199(6)
7.4 Bias and Mean Squared Error
205(2)
7.5 Best Estimators
207(7)
7.6 Consistent Estimators
214(4)
7.7 Bayes Estimators
218(9)
Problems
222(5)
8 Confidence Regions
227(19)
8.1 Definition and Construction
227(6)
8.2 Confidence Intervals in the Binomial Model
233(6)
8.3 Order Intervals
239(7)
Problems
243(3)
9 Around the Normal Distributions
246(14)
9.1 The Multivariate Normal Distributions
246(3)
9.2 The x2-, F- and t-Distributions
249(11)
Problems
256(4)
10 Hypothesis Testing
260(29)
10.1 Decision Problems
260(5)
10.2 Neyman-Pearson Tests
265(6)
10.3 Most Powerful One-Sided Tests
271(3)
10.4 Parameter Tests in the Gaussian Product Model
274(15)
Problems
284(5)
11 Asymptotic Tests and Rank Tests
289(36)
11.1 Normal Approximation of Multinomial Distributions
289(7)
11.2 The Chi-Square Test of Goodness of Fit
296(7)
11.3 The Chi-Square Test of Independence
303(6)
11.4 Order and Rank Tests
309(16)
Problems
320(5)
12 Regression Models and Analysis of Variance
325(32)
12.1 Simple Linear Regression
325(4)
12.2 The Linear Model
329(5)
12.3 The Gaussian Linear Model
334(8)
12.4 Analysis of Variance
342(15)
Problems
351(6)
Solutions 357(28)
Tables 385(6)
References 391(4)
List of Notation 395(4)
Index 399
Hans-Otto Georgii, Ludwig-Maximilians-Universität Munich, Germany.
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