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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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Diffuse x-ray scattering from GaN epitaxial layers
Barchuk, Mykhailo ; Holý, Václav (advisor) ; Caha, Ondřej (referee) ; Pietsch, Ulrich (referee)
Real structure of heteroepitaxial GaN and AlGaN layers is studied by diffuse x-ray scattering. A new developed method based on Monte Carlo simulation enabling to determine densities of threading dislocations in c-plane GaN and stacking faults in a-plane GaN is presented. The results of Monte Carlo simulations are compared with ones obtained by use of other conventional techniques. The advantages and limitations of the new method are discussed in detail. The methods accuracy is estimated as about 15%. We have shown that our method is a reliable tool for threading dislocations and stacking faults densities determination.
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Sequential Monte Carlo Methods
Sobková, Eva ; Zikmundová, Markéta (advisor) ; Prokešová, Michaela (referee)
Monte Carlo methods are used for stochastic systems simulations. Sequential Monte Carlo methods take advantage of the fact that observations are coming sequentially. This allows us to refine our estimate sequentially in time We introduce a State Space Model as a Hidden Markov Model. We describe Perfect Monte Carlo Sampling, Importance Sampling, Sequential Importance Sampling and discuss advantages and disadvantages of these methods. This discussion brings us to add a resampling step in Sequential Importance Sampling and introduce Particle Filter and Particle Marginal Metropolis-Hastings algorithm. We choose a Hidden Markov Model used for stochastic volatility modeling and make a simulation study in Wolfram Mathematica, version 8.
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EV smart charging and BESS in increasing the PV hosting capacity of distribution networks
Filip, Robin ; Lehtonen, Matti (referee) ; Paar, Martin (advisor)
Diplomová práce se zabývá dopadem nabíjení elektrických vozidel a bateriových úložišť na schopnost distribučních sítí nízkého napětí absorbovat fotovoltaické systémy. Převážně venkovské, příměstské a převážně městské regiony s různými stupni penetrace nekontrolovaně i kontrolovaně nabíjených elektromobilů jsou analyzovány Monte Carlo simulacemi. Hostingová kapacita je také analyzována, jestliže jsou elektrická vozidla jak nahrazena, tak doplněna domácími bateriovými úložišti. Práce je zakončena krátkou analýzou využitelnosti BESS.
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Econometric methods of change detection
Dvoranová, Romana ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
Detection of structural changes in time series is a topic with increasing pop- ularity among econometricians over the last decades. The main aim of this thesis was to review and compare the classical and modern econometric meth- ods of structural change detection and unit root testing. A recent method for testing a one-time break in at most linear trend function of a series without prior knowledge about the stationary or unit root nature of the error compo- nent proposed by Perron and Yabu (2009b) was studied. Subsequently, it was combined with the unit root test that allows for a break in trend proposed by Kim and Perron (2009) to examine the nature of the error component. All the methods for change detection and unit root testing were compared in a Monte Carlo simulation study that indicated significant improvement in power of the Perron-Yabu and Kim-Perron tests against most alternatives compared to the classical methods. However, all tests demonstrated poor performance in case of a quadratic trend function. Finally, the tests were employed in a practical ex- ample to examine the properties of the quarterly GDP time series of the Czech Republic. 1
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Actuarial and Exposure-based Models for Hail Peril
Drobuliak, Matúš ; Pešta, Michal (advisor) ; Hlubinka, Daniel (referee)
Title: Actuarial and Exposure-based Models for Hail Peril Author: Bc. Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: This thesis covers an introduction to catastrophe modelling and focuses on statistical methods for extreme events. This includes methods of estimating parameters of claim distribution with a focus on probability weighted moments estimation technique. Furthermore, times series modelling, skew t-distribution, and two model clustering techniques are examined as well. This is later utilised in the practical application part of this thesis, which uses real data provided by an insurance company operating in the Czech Republic. Probability distribution fitting of large claims caused by hailstorms and Monte Carlo simulation of future losses are demonstrated later. Keywords: Catastrophe modelling, Hail peril, Probability weighted moments, Extreme events, ARMA-GARCH, Monte Carlo simulation iii
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Theoretical description and simulation of polymer network formation
Premus, Jan ; Šomvársky, Ján (advisor) ; Dušek, Karel (referee)
One of methods for description of formation and structure of polymer ne- tworks is used in the work - combination of chemical kinetics and theory of branching processes (TVP) with correlations to neighbors. Main output of this work is computer program, whose purpose is setting up of rooted fragments of given size, differential equations for their concentrations and calculation of se- lected structural parameters using TVP. Gel points for systems formed by three and fourfunctional monomer and combination of two and threefunctional mono- mer were computated in this way. Chemical simulation of molecules was used as reference value. Larger correlation distance (larger size of fragments) led to more accurate results. Calculation of system parameters using TVP allowed study of gel parameters, concentrations of elastically active chains for all studied systems is shown in the work. 1
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Optimization of scintillation detector for detection of low energy signal electrons in electron microscopy
Tihlaříková, Eva ; Kadlec, Jaromír (referee) ; Uruba, Václav (referee) ; Neděla, Vilém (advisor)
The dissertation thesis deals with optimization of the scintillation detector for efficient detection of low energy signal electrons in a specimen chamber of a scanning electron microscope. The solution was based on the study of signal electron energy loss mechanisms during their interaction with a conductive layer and a scintillator that can be studied using simulations based on the stochastics Monte Carlo methods. Based on test simulations and their comparison with experimental data, the ideal Monte Carlo software was chosen and used for the study of signal electron energy losses during their transport through the conductive layer as well as following interaction with scintillator, in dependency on the signal electron energy. Simulation results allowed to define criteria for the optimization of the conductive layer. According to these parameters, the optimized layers were deposited on the surface of different scintillators and experimentally tested in the scintillation detector of the scanning electron microscope. Experimental measurements allowed to verify accomplished simulations and provide new information about impact of materials and thicknesses of conductive layers in combination with materials of scintillators and light guides. The increase of the detection efficiency of the scintillation detector equipped with optimised conductive layers and its capability to detect low energy signal electrons were experimentally proved.
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Application of Monte Carlo simulations in banking
Slanina, Šimon ; Teplý, Petr (advisor) ; Fičura, Milan (referee)
A vigorous advancement in the field of information technologies allows practical use of sophisticated, computing power consuming methods. One of these is the Monte Carlo simulations method, which relies on generating an immense number of stochastic scenarios and can effectively solve problems in areas such as physics or mathematics. Entities in the banking sector are constantly exposed to many kinds of risks, for instance the occurrence of negative interest rates. These risks need to be taken into account, monitored, measured and managed. Even the Monte Carlo method, usable in banking for risk measurement, has its weaknesses that need to be considered, and requires certain conditions to be met. It is crucial to correctly approximate the probability distribution and to create a sufficient number of random scenarios, to use a reliable random number generator and to bear in mind any possible sequential dependencies amongst the input data. In the practical part of this work, I analyzed the development of the London Interbank Offered Rate with a three-month maturity based on the US dollar during the years 2000 to 2016 and, using the Monte Carlo method, I tried to predict its future development as well. I came to the conclusion that the method should be used for forecasting in shorter time horizons, considering it provides significantly wider ranges of the rate's possible values at all probability levels while forecasting for longer time horizons. Via stress test, I also found that the method I applied doesn't really reflect rare short-term shocks in the resulting predictions. Neither the Monte Carlo method nor the TRADING ECONOMICS website anticipate the LIBOR USD 3M rate to fall below zero during the time horizon ending in 2020.
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Cost planning of PPP projects in the Czech Republic
Ehrenberger, Marek ; Teplý, Petr (advisor) ; Chytilová, Julie (referee)
English The thesis explores the topic of cost planning of Public-Private-Partnership (PPP) projects in the Czech Republic, especially with respect to institutional settings and road infrastructure. First, the PPP concept is introduced from a theoretical perspective and compared to traditional public procurement. Then the financing of PPP projects is discussed in the context of project finance and the European PPP market. The main part of the thesis focuses on public procurement of road infrastructure and the advantages of the PPP organizational structure. Initially, flaws of the procurement institutions are identified and a number of solutions suggested. The solutions cover four main areas: improvement of procurement laws, better qualifications of public officials, strategic planning of needed roads and asset management perspective on the existing infrastructure. The question whether Czech institutions are hindering the potential of PPP projects is answered positively. Follows a thorough empirical analysis of a World Bank PPP model for highways through a Monte Carlo simulation. A particular case of R35 motorway is evaluated as a PPP project and key drivers of public and private NPV are identified and compared across three different scenarios. Heavyweight traffic intensity, its toll revenue and...
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