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Genetical algorithms and their use in optimization
Krtek, Jiří ; Antoch, Jaromír (advisor) ; Dupač, Václav (referee)
In the present work we deal with a branch of stochastic optimization algorithms, so called genetic algorithms. In the first chapter we can find description of a run of the genetic algorithm and the main operations which route searching of a feasible solution set, i.e. crossover and mutation. There is not absent a simple example, whereon reader can make sense of the presented operations. There is a short chapter devoted to theory of genetic algorithms which follows section describing various improvements of the basic algorithm, e.g. the Gray code. A real optimization problem is introduced in the third and also the last chapter. We have solved it using the theory of Markov decision processes for modeling a queuing system and by using genetic algorithms for finding optimum. We have also looked for optimum via a specialized algorithm. Both approaches are compared in the end of this chapter. All calculations have been implemented in the Fortran language.
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Anotační grafy a Bayesovské sítě
Čoupková, Evženie ; Studený, Milan (advisor) ; Antoch, Jaromír (referee)
There are different models, which describe conditional independence induced by multivariate distributions. Models such as Undirected Graphs, Directed Acyclic Graphs, Essential Graphs and Annotated Graphs are introduced and compared in this thesis. The focus is put on annotated graphs. It is shown that annotated graphs represent equivalence classes of DAG-representable relations. An algorithm for reconstruction of an annotated graph from an essential graph as well as the algorithm for the inverse procedure are given. Some properties of a characteristic imset, which is a non-graphical representation, are discussed. A relationship between annotated graphs and characteristic imsets is investigated, an algorithm, which reconstructs an annotated graph from a characteristic imset is given. Powered by TCPDF (www.tcpdf.org)
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Extreme Value Theory in Actuarial Sciences
Jamáriková, Zuzana ; Mazurová, Lucie (advisor) ; Antoch, Jaromír (referee)
This thesis is focused on the models based on extreme value theory and their practical applications. Specifically are described the block maxima models and the models based on threshold exceedances. Both of these methods are described in thesis theoretically. Apart from theoretical description there are also practical calculations based on simulated or real data. The applications of block maxima models are focused on choice of block size, suitability of the models for specific data and possibilities of extreme data analysis. The applications of models based on threshold exceedances are focused on choice of threshold and on suitability of the models. There is an example of the model used for calculations of reinsurance premium for extreme claims in the case of nonproportional reinsurance.
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Estimators of variance function in nonparametric regression
Hyklová, Bronislava ; Hušková, Marie (advisor) ; Antoch, Jaromír (referee)
The thesis studies variance function estimation in nonparametric regression model. It focuses on local polynomial estimators particularly. Exact expressions of conditional variance function estimator bias and covariance are derived and important asymptotical aproximations of these characteristics are also provided. Further the EBBS method for bandwidth selection and Dette's homoscedasticity test are described. Results of Prague Klementinum data processing are presented at the end of the thesis.
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Reliability of systems with redundant subsystems and/or elements
Čáha, Pavel ; Antoch, Jaromír (advisor) ; Hurt, Jan (referee)
The thesis deals with the basic notions of the (system) reliability theory as e.g., failure, time to failure, reliability function, mean time to failure, intensity of failures, etc. It also describes probability distributions that are frequently used in the field of (system) reliability. Fourth chapter is focused on the reliability of basic systems as, e.g., serial, prallel, circle and star, using Boolean algebra and Markov chains. The last part of the thesis describes the simulation of complex systems. This part also includes two programmes. The first one enables a simulation of reliability of basic systems and the second reliability of the network of the building MFF UK, Karlín. Powered by TCPDF (www.tcpdf.org)
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Skew normal distribution
Helebrand, František ; Hudecová, Šárka (advisor) ; Antoch, Jaromír (referee)
Title: Skew normal distribution Author: František Helebrand Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Šárka Hudecová, Ph.D., Department of probability and mathematical statistics Abstract: In this paper, the skewed normal probability distribution is studied. First, the density is proposed and the basic properties of this distribution are proved. Then the thesis deals with the moment and cumulative generating functions. These functions are used in deriving the mean, variance and skewness of the skew normal distribution. In the third chapter, two parameter estimators are proposed and their properties are derived. Finally, these estimators are empirically investigated in a simulation study and on real data. Keywords: normal distribution, skewness, point estimators 1
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