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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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Fitting of Probability Distributions for Applications
Pavlíčková, Lenka ; Bednář, Josef (referee) ; Karpíšek, Zdeněk (advisor)
The diploma thesis describes the bootstrap method and its applications in the confidence intervals generation, in the testing of statistical hypotheses and in the regression analysis. We present the confidence interval for individual value. Further the method of discrete probability estimation of the categorical quantity is presented, making use the gradient and the line estimate.
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Subjective quality evaluation of video sequences
Krmela, Tomáš ; Fliegel, Karel (referee) ; Polák, Ladislav (advisor)
This master´s work is focused on the comparison of subjective assessment of the quality of video sequences. In this study, data are obtained by hardware and sofware techniques and they are compared. In the introduction, methods of video compressions are described. The main part of this work deals wtih the exploring of different methods of subjective assessment of the quality of video sequences. Finally, obtained results from different methods, are evaluated and discussed.
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Bootstrap Method and its Application
Pavlíčková, Lucie ; Lacinová, Veronika (referee) ; Karpíšek, Zdeněk (advisor)
The diploma thesis describes the bootstrap method and its applications in the estimate accuracy statement, in the confidence intervals generation and in the testing of statistical hypotheses. Further the method of the discrete probability estimation of the categorical quantity is presented, making use the gradient of the quasi-norm hereof distribution. On concrete examples the bootstrap method is applied in the confidence intervals forming of the categorical quantity probability function. The diploma thesis was supported by the project of MŠMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production", by the grant of Grant Agency of the Czech Republic (Czech Science Foundation) reg. no. 103/08/1658 "Advanced optimum design of composed concrete structures" and by the research plan of MŠMT of the Czech Republic no. MSM0021630519 "Progressive reliable and durable structures".
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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 differences and ratios of proportions
Krnáč, Ľuboš ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
The Bachelor thesis deals with the creation of confidence intervals for diffe- rence of parameters of two distributions. In the first part we consider the problem of making such confidence intervals for differences. Then we try to find sufficient conditions for MOVER, which leads to new, non-trivial confidence intervals for difference of parameters of two distributions. These confidence intervals have im- proved and desired properties. There are also examples of usage of MOVER, and possible difficulties. The third section contains graphs of coverage probabili- ties for different input intervals. These graphs are made to show different levels of achieved coverage probabilities for some input intervals, namely Clopper-Pearson, Wald, Wilson and logit. 1
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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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