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Comparison of tests on null correlation between two normal random variables
Kalenský, Vít ; Žák, Libor (referee) ; Hübnerová, Zuzana (advisor)
This thesis deals with the comparison of the tests of the correlation coecient of two normal random variables using T statistics, Fisher's transformation, Hotelling transformation and Haddad-Provost's statistics. It contains the derivation of the tests and their power function, which then compares each other and with the values obtained from the simulated random samples in program MATLAB. Finally the thesis depicts and describe the results. There is also the theoretical introduction to the topic.
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Integer Optimization for Transportation Problems
Cabalka, Matouš ; Žák, Libor (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems with emphasis on traveling salesman problem. Brief introduction to the history is followed by theoretical part describing linear programming, integer programming and formulation of traveling salesman problem. Description of data preprocessing is included. Finally computational results are discussed and evaluated.
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Application of cluster analysis to real data
Onderlička, Tomáš ; Popela, Pavel (referee) ; Žák, Libor (advisor)
This bachelor's thesis deals with finding similar scenarios in the waste management acquired by an optimization tool NERUDA. Cluster analysis, a tool that identifies related objects and classifies them in groups (clusters), is used for this purpose. The aim of this thesis is to review basic algorithms of cluster analysis and to develop a software that implements them. The software is then used to cluster real data from NERUDA which is followed by an assessment of the obtained clusters.
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Models and methods for routing problems
Nevrlý, Vlastimír ; Žák, Libor (referee) ; Popela, Pavel (advisor)
This master's thesis deals with mathematical model building for routing problems and ways to solve them. There are discussed and implemented deterministic and heuristic approaches that are suitable to be utilized. A big effort is put into building of the mathematical model describing a real world problem from the field of waste management. Appropriate algorithms are developed and modified to solve a particular problem effectively. An original graphical environment is created to illustrate acquired results and perform testing computations.
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Design of Experiment
Sabová, Iveta ; Žák, Libor (referee) ; Bednář, Josef (advisor)
This thesis deals with the possibility of applying the method of Design of Experiments (DoE) on specific data. In the first chapter of theoretical part, this method is described in detail. The basic principles and guidelines for the design of the experiment are written there. In the next two chapters, factorial design of the experiment and response surface design are described. The latter one includes a central composite design and Box-Behnken design. The following chapter contains practical part, which focuses on modelling firing range of ball from a catapult using the above three types of experimental design. In this work, the models are analysed together with their different characteristics. Their comparison is made by using prediction and confidence intervals and by response optimizing. The last part of the thesis comprises overall evaluation.
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Statistical Classification Methods
Barvenčík, Oldřich ; Žák, Libor (referee) ; Michálek, Jaroslav (advisor)
The thesis deals with selected classification methods. The thesis describes the basis of cluster analysis, discriminant analysis and theory of classification trees. The usage is demonstrated by classification of simulated data, the calculation is made in the program STATISTICA. In practical part of the thesis there is the comparison of the methods for classification of real data files of various extent. Classification methods are used for solving of the real task – prediction of air pollution based of the weather forecast.
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Probit Analysis and its Theoretical Properties
Bojanovská, Hana ; Žák, Libor (referee) ; Bednář, Josef (advisor)
The diploma thesis deals with a theoretical description and practical use of probit analysis, which is a part of survival analysis. The thesis shows different probit models, their differences and appropriateness on analised data. The used data belong to the molecular diagnostic area and are provided by Genex CZ company. The result is an analysis of probit analysis output data from Minitab 14 software. The thesis was supported by project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.
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Time Series Analysis and Comparison by Means of Statistical Methods
Kopecký, Radek ; Bednář, Josef (referee) ; Žák, Libor (advisor)
The aim of the thesis mainly is to understand an issue of time series analysis. There are many methods in time series analysis, but purpose of this analysis persists the same, which is a construction of sufficient model of time series and his application in forecasting of time series. We have to make a basic identification of time series to establish right process in model constructing. The first and the second chapter is devoted to this basic identification. There are many methods, how we said before, for constructing of concrete model. In this thesis, exactly in the third chapter, we introduce one of the most flexible methodology of model constructing. That is The Box-Jenkins methodology, which was defined in 1976 by these men. In the last chapter we try to put to use insight in the issue of time series analysis for comparison and separation of the space of time series and this comparison use for the right interpretation of the parameters of time series model. The diploma project was supported by project from MSMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production".
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The Fourier Series and Its Properties
Sladká, Pavla ; Žák, Libor (referee) ; Štarha, Pavel (advisor)
The functional series, and especially the Fourier series, are an important mathematical apparatus exploited in the various technical branches. A very essential group of the functional series are the power series, which are applied because of their simplicity for solving of the many problems. An expansion of the function to the power series, i. e. the Taylor expansion, whose sum is the expanded function. These expansions are suitable for evaluation of operations, such as calculation of functional values, limits, derivatives and integrals. Calculations of these expansions are easier than of the functions theirself. The Fourier series are used for studies of events with periodic character. An advantage of the Fourier series is the fact, that the requirements for convergency are weaker than in case of the Taylor expansions. Likewise, calculation of the coefficients can be more simple than in the Taylor expansions. Expansions of functions to the Fourier series are used especially for solving ordinary and partial differential equations. This method of solving is known as the Fourier method or the Fourier method of variable separation.
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