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Parameter estimation of random variables distribution
Šimková, Barbora ; Mošna, František (advisor) ; Novotná, Jarmila (referee)
of the bachelor's thesis Title: Parameter estimation of random variables distribution Author: Bc. Barbora Šimková Department: Department of Mathematics and Mathematical Education Supervisor: RNDr. František Mošna, Dr. Abstract: The subject of this thesis is to compare basic methods by which it is possible to calculate point estimates of discrete and continuous probability distributions. The work deals with the analysis of the two methods - the method of moments and maximum like- lihood method. These methods are used for point estimates of probability distributions parameters. The method of moments studies the comparison between the theoretical and sample moments of a random variable. The method of maximum likelihood is an- other alternative for the calculation of point estimates, which uses the classical approach of finding the maximum of a function, using the properties of random selection. These methods of calculation are based on statistical methods and could be used as an inter- isting extencion of the basic course on probability and statistics at Charles University's Faculty of Education. The work is an overview of the estimated parameters of the basic distribution and compares the quality of two basic methods for their estimation. Keywords: parameter estimation, distribution of random...
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Parameter estimation of random variables distribution
Šimková, Barbora ; Mošna, František (advisor) ; Novotná, Jarmila (referee)
of the bachelor's thesis Title: Parameter estimation of random variables distribution Author: Bc. Barbora Šimková Department: Department of Mathematics and Mathematical Education Supervisor: RNDr. František Mošna, Dr. Abstract: The subject of this thesis is to compare basic methods by which it is possible to calculate point estimates of discrete and continuous probability distributions. The work deals with the analysis of the two methods - the method of moments and maximum like- lihood method. These methods are used for point estimates of probability distributions parameters. The method of moments studies the comparison between the theoretical and sample moments of a random variable. The method of maximum likelihood is another alternative for the calculation of point estimates, which uses the classical ap- proach of finding the maximum of a function, using the properties of random selection. These methods of calculation are based on statistical methods and could be useful for extending the basic course on probability and statistics at Charles University's Fac- ulty of Education. The work is an overview of the estimated parameters of the basic distribution and compares the quality of two basic methods for their estimation. Keywords: parameter estimation, distribution of random variables, maximum...
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Control of Linear Inverted Pendulum Exhibition Model
Vávra, Patrik ; Sova, Václav (referee) ; Brablc, Martin (advisor)
The main aim of this bachelor thesis is to create robust linear inverted pendulum control. After system identification comes the creation of regulators from which the most suitable is chosen for the final control of the pendulum. Another point of thesis is to develop a swing-up controller that takes care of swinging the pendulum into an unstable position and swing-down controller to stabilize the pendulum as quickly as possible in a stable pendulum position. The following sections of the thesis include the design of the control structure, safety measures and evaluation of the performed testing.
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Interest Rates
Holotňáková, Dominika ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
This thesis is focused on the study of interest rates, It consists of four chapters. The first chapter provides introduction to this issue, presents basic terminology and different method of interest rate process. The second chapter re- presents theoretical one-factor and two-factor models of interest rates, it is mainly aimed at Vasicek, Dothan and Cox-Ingersoll-Ross model, which are used in the practical part. The third chapter is devoted to internal bank policy, describing the most important factors influencing amount of interest rate and credit limit. The last part of the paper is the practical application of one-factor models on real data. At the beginning of the chapter, we describe methods of parameters esti- mation, which are used for individual models. Numerically estimated parameters are inputs for simulations of yield curves by these models. 1
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General skew-probability distributions
Václavík, Jiří ; Lachout, Petr (advisor) ; Dostál, Petr (referee)
In the present work we study families of skew-probability distributions. We will gradually build concept of families of more and more general distributions. For us the most important ones are skew normal distribution, elliptical distri- bution and skew elliptical distribution. On the each of them we will present basic properties and visualize particular examples. At the end we will generate realizations of variates and propose how to estimate the original distribution.
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Advanced signal processing methods in dynamic contrast enhanced magnetic resonance imaging
Bartoš, Michal ; Flusser,, Jan (referee) ; Mlynárik,, Vladimír (referee) ; Jiřík, Radovan (advisor)
Tato dizertační práce představuje metodu zobrazování perfúze magnetickou rezonancí, jež je výkonným nástrojem v diagnostice, především v onkologii. Po ukončení sběru časové sekvence T1-váhovaných obrazů zaznamenávajících distribuci kontrastní látky v těle začíná fáze zpracování dat, která je předmětem této dizertace. Je zde představen teoretický základ fyziologických modelů a modelů akvizice pomocí magnetické rezonance a celý řetězec potřebný k vytvoření obrazů odhadu parametrů perfúze a mikrocirkulace v tkáni. Tato dizertační práce je souborem uveřejněných prací autora přispívajícím k rozvoji metodologie perfúzního zobrazování a zmíněného potřebného teoretického rozboru.
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Design of embedded system for control of educational model of rotary pendulum
Jajtner, Jan ; Chalupa, Jan (referee) ; Grepl, Robert (advisor)
The basic aim of this work is to improve existing model of rotational inverted pendulum by adding new mechanical features, implement the control algorithm to dsPIC microcontroller and develop related control electronics thus extending the functionality of current model while making it more compact. The work contains derivation of dynamic equations both by means of analytical methods and multi-body formalism of SimMechanics. These are used to design a state controller stabilizing the pendulum in inverse position. In addition, parameters of the system are being estimated experimentally. Swing-up controller is developed to drive the pendulum to unstable position. Various state estimators are added to controller to improve the control process while comparing their overall performance. The last point is devoted to development of superior state-automaton designed to switch between different regulating modes including fail-detection algorithms providing smooth operation of the model.
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Design of dynamic models for traction control of experimental vehicle
Jasanský, Michal ; Porteš, Petr (referee) ; Grepl, Robert (advisor)
The Master's thesis deals with the simulations kinematics and dynamics of experimental four-wheeled vehicle with all-wheel steering and all-wheel drive. Suggestion of vehicle stability systems ABS/ASR for traction control is included. There are several dynamics models with their comparison. The estimation of important vehicle parameters is implemented. Based on knowledge the simple vehicle stability system ABS/ASR is created.
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HIL Simulation of Electronic Throttle
Maliszewski, Michal ; Chalupa, Jan (referee) ; Sova, Václav (advisor)
This thesis deals with the Hardware in the Loop (HIL) simulation of an electronic throttle. In the following text its mathematical model for different options of friction and hardstops is deduced. Model parameters were obtained by measurement on the real throttle. In the next step the thesis aims on designing the suitable control algorithm, which is used for own HIL simulation. The output of the thesis is the choice of the best model with respect to accuracy and computation time of the simulation.
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