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Lecturer(s)
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Javůrek Milan, doc. Ing. CSc.
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Marek Jaroslav, Mgr. Ph.D.
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Course content
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1. Repetition and deepening knowledge of probability theory. Kolmogorov definition of probability. Random variable. The distribution function of the random variable and random vector. The most important distributions. 2. Descriptive statistics. Population and Sample. Histogram and Freguency Polygons. Cumulative-Frequency Distributions. Galton's Ogives. Boxplot. 3. Types of variables (nominal, ordinal, quantitative, dichotomic). Random Sample. Transformation od variables. Standardized variable. The mean, Median, Mode, and Other measures of Central Tendency. The Standard Deviation and Other Measures of Dispersion. Moment, Skewness, and Kurtosis. The empirical Relation between the Mean, Median, and Mode. Empirical discribution Function. 4. Sampling Theory of Correlation. Correlation Coefficient, Pearson correlation coefficient, Spearman's rank correlation coefficient, Kendall tau rank correlation coefficient. Variance matrix. Confidence domain. 5. Statistical Decision Theory. Statistical Hypothesis. Contingence Tables. The chi-Square Test for Goodness of Fit. Nonparametric tests. The Runs Test for Randomness. 6. Consumer price index. Basket of Goods. Paasche, Laspeyres and Fisher indices. 7. Time Series. Decomposition. Trend, Cyclical, Seasonal and Irregular Components. Moving-average models. Simple exponential smoothing. Technical Indicators. 8. Linear Regression: history and development of algorithms: Boskovitsch method, Lambert's method, Laplace's method, Least Squares Method. 9. Nonlinear regresssion. Orthogonal regression. Regression models with constraints. 10. Analysis of Variance. One-way classification. Design of experiment. 11. Statistical Process Control and Process Capability. Sampling plans. 12. Principal component analysis. Factor analysis. Linear discriminant analysis. 13. Cluster analysis. Measuring of distances. Hierarchical and Nonhierarchical clustering.
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Learning activities and teaching methods
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Dialogic (discussion, interview, brainstorming)
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Learning outcomes
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The aim of the course is to acquaint the students with theory of probability and statistical principles in order to apply it in real situations.
Student will be able to use statistical methods and theory of probability in real situations.
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Prerequisites
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Good mathematical skills. Good integral and differential calculus knowledge.
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Assessment methods and criteria
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Oral examination, Written examination
The credit is granted upon completion of following conditions: active participation in seminars (labs); max. 3 absences. The examination comprises of three parts: written theory and practical tests; at least 51% success rate in each part is required; successful speaking test.
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Recommended literature
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Fahrmeir und koll. Statistik. Springer - Verlag. Berlin, 2004.
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Kubanová, J., Linda, B. Sbírka příkladů z pravděpodobnosti. Statis, 2004.
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Kubanová, J. Statistické metody pro ekonomickou a technickou praxi. Statis, 2004.
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Sirvastava, M., S. Methods of multoivariate statistics. Wiley, New York, 2002.
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