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Optimization Models in Energy Production
Němcová, Lucie ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This bachelor's thesis focuses on optimization of a boiler's size of a waste incineration plant from an economic point of view. The problem was approximated by discretization because random parameters with normal distribution occured in the incineration plant model. To evaluate the quality of such approximation there were created confidence intervals using random sample information, independent random number streams method and common random number streams method. Used methods were compared and the smallest number of scenarios that aproximates the problem "well enough" was proposed in the last part of this thesis.
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Optimization Models in Energy Production
Němcová, Lucie ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This bachelor's thesis focuses on optimization of a boiler's size of a waste incineration plant from an economic point of view. The problem was approximated by discretization because random parameters with normal distribution occured in the incineration plant model. To evaluate the quality of such approximation there were created confidence intervals using random sample information, independent random number streams method and common random number streams method. Used methods were compared and the smallest number of scenarios that aproximates the problem "well enough" was proposed in the last part of this thesis.
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Continuity correction
Štěpán, Marek ; Omelka, Marek (advisor) ; Maciak, Matúš (referee)
For an approximation of discrete random variable, which is the sum of n inde- pendent, identically distributed discrete random variables, we can use the central limit theorem. However, it turns out that we can refine this approximation by applying continuity correction. This term is explained in the thesis, and it is illustrated several ways how the continuity correction can be derived. There is also a numerical comparison of the approximation error for the binomial distribu- tion approximation by the normal distribution with the correction for continuity and approximation without the correction. There are also described confidence intervals and χ2 test of independence in contingency tables in which continu- ity correction are used. On simulations for various parameters, we will test the properties of these intervals (true confidence level and length) and tests (actual significance level and power).
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Confidence Intervals for Binomial Parameters
Rusá, Pavla ; Kulich, Michal (advisor) ; Maciak, Matúš (referee)
The Bachelor thesis deals with the construction of confidence intervals for the parameter of the Binomial distribution. In the first part of the thesis we deal with the relationship between hypotheses testing and confidence in- tervals. The methods mentioned in this thesis are based on this relationship. The next part is devoted to the Clopper-Pearson method and its possible improvements which were made by Sterne, Crow, Blyth and Still. The gra- phical approach of Schilling and Doi is also worth noticing. Afterwards we present the methods based on the Normal approximation, particularly the Wilson method and the Wald method. Finally, all the methods mentioned in this thesis are compared in terms of coverage probability. 1
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Analysis of household consumption in the EU
Kolman, Martin ; Bílková, Diana (advisor) ; Malá, Ivana (referee)
The goal of this work is to analyze the evolution of household consumption of the states in the EU. The consumption will be researched in the view of classification COICOP, which is the classification of individual consumption by purpose. After mapping of this evolution the estimation of future values will be done from known time series. This estimation will be performed by two different ways. First one will respect the composition of household consumption in sections of classification COICOP. The second one will only work with time series of average consumption for all sections together. To compare the states cluster analysis will be done. This analysis will be done by two ways again. First one will be aimed to analyze the current situation and the second one will be aimed to analyze the evolution of household consumption. Instead of Microsoft Excel STATGRAPHICS X64 CENTURION and SPSS will be used in this thesis. Household consumption prognosis is the main benefit of this thesis. This prognosis is made for all sections of COICOP. Analysis has shown, that the consumption should rise in future. There are few exceptions, mainly countries with not good economic situation as Greece.
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