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Stochastics: Introduction to Probability and Statistics [Kõva köide]

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  • Formaat: Hardback, 379 pages, kõrgus x laius: 240x170 mm, kaal: 635 g
  • Sari: De Gruyter Textbook
  • Ilmumisaeg: 27-Feb-2008
  • Kirjastus: De Gruyter
  • ISBN-10: 3110191458
  • ISBN-13: 9783110191455
Teised raamatud teemal:
Stochastics: Introduction to Probability and StatisticsSuurem pilt
  • Formaat: Hardback, 379 pages, kõrgus x laius: 240x170 mm, kaal: 635 g
  • Sari: De Gruyter Textbook
  • Ilmumisaeg: 27-Feb-2008
  • Kirjastus: De Gruyter
  • ISBN-10: 3110191458
  • ISBN-13: 9783110191455
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783110191455.html

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.

Arvustused

"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 work."Vladimir P. Kurenok in: Mathematical Reviews 2009b "The book is well-written and mathematically oriented students and researchers will certainly find that it provides a high level introduction to probability theory and mathematical statistics."In: EMS Newsletter 9/2008

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 work.Vladimir P. Kurenok in: Mathematical Reviews 2009b The book is well-written and mathematically oriented students and researchers will certainly find that it provides a high level introduction to probability theory and mathematical statistics.In: EMS Newsletter 9/2008

Preface v
Mathematics and Chance 1(4)
Probability Theory
5(180)
Principles of Modelling Chance
7(19)
Probability Spaces
7(7)
Properties and Construction of Probability Measures
14(5)
Random Variables
19(7)
Problems
23(3)
Stochastic Standard Models
26(24)
The Uniform Distributions
26(3)
Urn Models with Replacement
29(5)
Urn Models without Replacement
34(3)
The Poisson Distribution
37(2)
Waiting Time Distributions
39(5)
The Normal Distributions
44(6)
Problems
46(4)
Conditional Probabilities and Independence
50(40)
Conditional Probabilities
50(6)
Multi-Stage Models
56(7)
Independence
63(6)
Existence of Independent Random Variables, Product Measures
69(4)
The Poisson Process
73(5)
Simulation Methods
78(4)
Tail Events
82(8)
Problems
84(6)
Expectation and Variance
90(27)
The Expectation
90(8)
Waiting Time Paradox and Fair Price of an Option
98(7)
Variance and Covariance
105(3)
Generating Functions
108(9)
Problems
112(5)
The Law of Large Numbers and the Central Limit Theorem
117(32)
The Law of Large Numbers
117(12)
Normal Approximation of Binomial Distributions
129(7)
The Central Limit theorem
136(5)
Normal verus Poisson Approximation
141(8)
Problems
143(6)
Markov Chains
149(36)
The Markov Property
149(3)
Absorption Probabilities
152(5)
Asymptotic Stationarity
157(12)
Recurrence
169(16)
Problems
177(8)
Statistics
185(164)
Estimation
187(35)
The Approach of Statistics
187(4)
Facing the Choice
191(4)
The Maximum Likelihood Principle
195(6)
Bias and Mean Squared Error
201(2)
Best Estimators
203(6)
Consistent Estimators
209(4)
Bayes Estimators
213(9)
Problems
217(5)
Confidence Regions
222(19)
Definition and Construction
222(6)
Confidence Intervals in the Binomial Model
228(6)
Order Intervals
234(7)
Problems
238(3)
Around the Noraml Distributions
241(14)
The Multivariate Normal Distributions
241(3)
The Χ2-, F-and t-Distributions
244(11)
Problems
251(4)
Hypothesis Testing
255(28)
Decision Problems
255(6)
Neyman-Pearson Tests
261(5)
Most Powerful One-Sided Tests
266(3)
Parameter Tests in the Gaussian Product Model
269(14)
Problems
278(5)
Asymptotic Tests and Rank Tests
283(35)
Normal Approximation of Multinomial Distributions
283(7)
The Chi-Square Test of Goodness of Fit
290(7)
The Chi-Square Test of Independence
297(6)
Order and Rank Tests
303(15)
Problems
313(5)
Regression Models and Analysis of Variance
318(31)
Simple Linear Regression
318(4)
The Linear Model
322(4)
The Gaussian Linear Model
326(8)
Analysis of Variance
334(15)
Problems
342(7)
Tables 349(6)
References 355(4)
List of Notation 359(4)
Index 363
Hans-Otto Georgii, Ludwig-Maximilians-University, Munich, Germany.