
Analysis of the robustness of the psychometric functions
Myšička, Pavel ; Děchtěrenko, Filip (advisor) ; Pilát, Martin (referee)
Psychophysics offers a wide range of experimental techniques to study human percep tion and often uses mathematical models to do so. Psychometrical function is a formal model of the relationship between intensity of stimulus and perception, that is used by psychophysics to model experimental data. There are various types of psychometric functions used in psychophysical practice. So far it is unknown whether use of different psychometric functions in model experiment data can influence the results of experiment. The goal of this work is to explore differences between commonly used psychometric func tions, prove if there are any differences between their ability to estimate psychometric data and if these differences are big enough so that researchers should pay attention to choice of psychometric function. 1


Parameter estimation of gamma distribution
Zahrádková, Petra ; Kulich, Michal (advisor) ; Hlávka, Zdeněk (referee)
It is wellknown that maximum likelihood (ML) estimators of the two parame ters in a Gamma distribution do not have closed forms. The Gamma distribution is a special case of a generalized Gamma distribution. Two of the three likeli hood equations of the generalized Gamma distribution can be used as estimating equations for the Gamma distribution, based on which simple closedform estima tors for the two Gamma parameters are available. Intuitively, performance of the new estimators based on likelihood equations should be close to the ML estima tors. The study consolidates this conjecture by establishing the asymptotic beha viours of the new estimators. In addition, the closedforms enable biascorrections to these estimators. 1


Use of Poisson distribution for prediction of sports matches results
Svoboda, Ondřej ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
The aim of this master thesis is to verify possibility to use Poisson distribution for predicting soccer matches. At first for analysis is applied the original model from English statisticians Mark J. Dixon and Stuart G. Coles from 1997. Thereafter the model is extended in the thesis. All models are based on the maximum likelihood method. Chosen league for deducing conclusions is the first English league  Premier League. The matches are played in the period from season 2004/2005 to half of season 2015/2016. For identification of models performance are used the most market odds from American bookmaker Pinnacle. In the theoretical part are described models and statistical methods that are used in the practical part. In the practical part are realized calculations. Counted performance of models is based on profit from market odds. In the period expost are calculated optimum model parameters that are used in the exante period, where is calculated performance of the model. The thesis answers question: Are these models gaining from public database effective in modern age?


Macroeconomic Analysis with Spatial Econometric Approaches
Macková, Simona ; Formánek, Tomáš (advisor) ; Tomanová, Petra (referee)
Spatial econometrics can bring a useful approach to macroeconomic analysis of regional data. This thesis delineates suitable crosssection data models regarding their geographical location. Neighbourhood relation is used for the analysis. The relation of neighbourhood among the regions is expressed using spatial weight matrix. We focus on spatial autocorrelation tests and introduce processes of finding a suitable spatial model. Further, we describe regression coefficients estimates and estimates of spatial dependence coefficients, especially method of maximum likelihood estimates. Besides illustrative examples we apply chosen basic spatial models on real macroeconomic data. We examine how they describe relation between household incomes, GDP and unemployment rate in western Europe. Results are compared with a linear regression model.


Estimation in continuous time Markov chains
Nemčovič, Bohuš ; Prokešová, Michaela (advisor) ; Kadlec, Karel (referee)
Title: Estimation in continuous time Markov chains Author: Bohuš Nemčovič Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this work we deal with estimating the intensity matrices of continu ous Markov chains in the case of complete observation and observation at selected discrete time points. To obtain an estimate we use the maximum likelihood met hod. In the second chapter we first introduce the general EM algorithm and then adjust it for finding the intensity matrix estimate based on observations at disc rete time points. In the last chapter we will illustrate the impact of the discrete step size on the quality of intensity matrix estimate. Keywords: Markov chains, intensity matrix, maximum likelihood estimation, EM algorithm 1


Statistical inference for Markov processes with continuous time
Křepinská, Dana ; Prokešová, Michaela (advisor) ; Lachout, Petr (referee)
Tato diplomová práce se zabývá odhadováním matice intenzit Markovova pro cesu se spojitým časem na základě diskrétně pozorovaných dat. Začátek práce je věnován jednoduššímu odhadu ze spojité trajektorie pomocí metody maximální věrohodnosti. Dále je zde popsán odhad z diskrétní trajektorie přes výpočet ma tice pravděpodobností přechodu. Následně je velmi podrobně rozebrán EM al goritmus, který předchozí odhad zpřesňuje. Na závěr teoretické části je uvedena metoda odhadu zvaná Monte Carlo Markov Chain. Všechny postupy jsou zároveň implementovány v počítačovém softwaru a prezentace jejich výsledk· je obsahem druhé části práce. V té jsou porovnané odhady pro denní, týdenní a měsíční po zorování a také pro pětiletou a desetiletou pozorovanou trajektorii. K výsledk·m jsou připojeny odhady rozptyl· a intervaly spolehlivosti. 1


Profile likelihood
Pejřimovský, Pavel ; Omelka, Marek (advisor) ; Jurečková, Jana (referee)
This thesis deals with a statistical method called pro le likelihood. We use it in estimating the unknown parameters in the presence of interfering parameters, compiling con dence intervals or testing hypotheses for example. Pro le likelihood is directly derived from the maximum likelihood method, which is one of the fundamental methods of mathematical statistics in estimating the unknown parameters. The maximum likelihood method is the base for asymptotic tests and their possible generalization on tests with nuisance parameters. In this work we show that there is some connection between the pro le likelihood and tests with nuisance parameters . It also illustrates the usage pro le credibility of the classic examples of the normal distribution. Powered by TCPDF (www.tcpdf.org)


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...


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...


Maximum likelihood estimators and their approximations
Tyuleneva, Anastasia ; Omelčenko, Vadim (advisor) ; Zvára, Karel (referee)
Title: Maximum likelihood estimators and their approximations Author: Anastasia Tyuleneva Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Vadym Omelchenko Abstract: Maximum likelihood estimators method is one of the most effective and accurate methods that was used for estimation distributions and parameters. In this work we will find out the pros and cons of this method and will compare it with other estimation models. In the theoretical part we will review important theorems and definitions for creating common solution algorithms and for processing the real data. In the practical part we will use the MLE on the case study distributions for estimating the unknown parameters. In the final part we will apply this method on the real price data of EEX A. G, Germani. Also we will compare this method with other typical methods of estimation distributions and parameters and chose the best distribution. All tests and estimators will be provided by Mathematica software. Keywords: parametr estimates, Maximum Likelihood estimators, MLE, Stable distribution, Characteristic function, Pearson's chisquared test, RaoCrámer. .
