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Stochastic programming models with applications
Novotný, Jan ; Michálek, Jaroslav (referee) ; Popela, Pavel (advisor)
Diplomová práce se zabývá stochastickým programováním a jeho aplikací na problém mísení kameniva z oblasti stavebního inženýrství. Teoretická část práce je věnována odvození základních přístupů stochastického programování, tj. optimalizace se zohledněním náhodných vlivů v modelech. V aplikované části je prezentována tvorba vhodných optimalizačních modelů pro mísení kameniva, jejich implementace a výsledky. Práce zahrnuje původní aplikační výsledky docílené při řešení projektu GA ČR reg. čís. 103/08/1658 Pokročilá optimalizace návrhu složených betonových konstrukcí a teoretické výsledky projektu MŠMT České republiky čís. 1M06047 Centrum pro jakost a spolehlivost výroby.
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Sampling procedures for inspection by attributes
Bartušek, Petr ; Fusek, Michal (referee) ; Michálek, Jaroslav (advisor)
This bachelor´s thesis deals with a description of sampling procedures for inspection by attributes. In the thesis there are described three discrete probability distributions – hypergeometric distribution, binomial distribution and Poisson distribution, including the convergence of their probability mass functions and cumulative distribution functions. The main aim of the thesis is a determination of a sampling plan for sampling procedures for inspection by attributes. The thesis is supplemented with three created programs, which are programmed in software Matlab.
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The choice of the best somatotype for a given sport using factor analysis
Bušík, Peter ; Fusek, Michal (referee) ; Michálek, Jaroslav (advisor)
This bachelor’s thesis deals with factor model, which is used for data reduction. The purpose is to find unobservable common factors, by which we are able to simply describe observed data. The thesis presents an estimation for parameters of factor analysis by the principal component method, a factor rotation by the varimax method and a way of estimating factor scores by the regression method. Using the computing programme STATISTICA, we apply the factor analysis on the data set, obtained in Korfball. Based on the results, we try to determine the best somatotype for players of this sport.
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Dependence Measures
Janda, Radek ; Fusek, Michal (referee) ; Michálek, Jaroslav (advisor)
This thesis focuses on characteristics of the dependence measures among random quantities, as well as its use in industry. The theoretical part focuses on examples of the characteristics used. Furthermore, the software Statistica is described here, for its possibilities of implementing such characteristics. On simple examples, the use of dependence measures is shown. In the practical part, the thesis focuses on statistical analysis of real industrial data, whilst implementing the theory mentioned above.
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The illustration of the law of large numbers by simulations
Chabičovský, Martin ; Kříž, Oldřich (referee) ; Michálek, Jaroslav (advisor)
Stochastic convergence, law of large numbers and central limit theorem is an important part of probability theory, which is often used in mathematical statistics. The aim of this work is to describe this theory and demonstrate it with examples and graphical simulation. In addition simulation of stochastic convergence, law of large numbers and central limit theorem for some discrete and continuous probability distribution the work contains several interesting simulations for example simulation of Galton's box, Buffon's needle problem and Bertrand's paradox. To create a graphic simulation were used programming language matlab.
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