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Stochastics : introduction to probability theory and statistics

Author: Hans-Otto Georgii
Publisher: Berlin ; New York : Walter De Gruyter, ©2008.
Series: De Gruyter textbook.
Edition/Format:   Book : English : [3rd ed.]
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: 288010383
Notes: Translated from the third German ed.: Stochastik : Einführung in die Wahrscheinlichkeitstheorie und Statistik, Berlin, Walter de Gruyter, Belin, 2007.
Description: ix, 370 p. : ill. ; 24 cm.
Contents: Mathematics and chance --
Principles of modelling chance --
Probability spaces --
Properties and construction of probability measures --
Random variables --
Uniform distributions --
Urn models with replacement --
Urn models without replacement --
Poisson distribution --
Waiting time distributions --
Normal distributions --
Conditional probabilities --
Multi-stage models --
Independence --
Existence of independent random variables, product measures --
Poisson process --
Simulation methods --
Tail events --
Expectation --
Waiting time paradox and fair price of an option --
Variance and covariance --
Generating functions --
Law of large numbers --
Normal approximation of binomial distributions --
Central limit theorem --
Normal versus Poisson approximation --
Markov property --
Absorption probabilities --
Asymptotic stationarity --
Recurrence --
Approach of statistics --Facing thechoice --
Maximum likelihood principle --
Bias and mean squared error --
Best estimators --
Consistent estimators --
Bayes estimators --
Definition and construction --
Confidence intervals in the binomial model --
Order intervals --
Multivariate normal distributions --
X[superscript 2]-, F- and t-distributions --
Decision problems --
Neyman-Pearson tests --
Most powerful one-sided tests --
Parameter tests in the Gaussian product model --
Normal approximation of multinomial distributions --
Chi-square test of goodness of fit --
Chi-square test of independence --
Order and rank tests --
Simple linear regression --
Linear model --
Gaussian linear model --
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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