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Modeling of scoring probability in sport
Hilscher, Ondřej ; Bednář, Josef (referee) ; Hrabec, Pavel (advisor)
This thesis aims for modelling of scoring probability in football. It describes necessary mathematical methods used in logistic regression model building and in basic statistical hypothesis tests. Afterwards the mathematical methods are used on available data from professional football matches. Resulting model uses shooting method, pitch location and simplified match situation as predictors.
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Modeling of scoring probability in sport
Hilscher, Ondřej ; Bednář, Josef (referee) ; Hrabec, Pavel (advisor)
This thesis aims for modelling of scoring probability in football. It describes necessary mathematical methods used in logistic regression model building and in basic statistical hypothesis tests. Afterwards the mathematical methods are used on available data from professional football matches. Resulting model uses shooting method, pitch location and simplified match situation as predictors.
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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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One factor models of interest rates
Jambor, Matúš ; Myška, Petr (advisor) ; Hurt, Jan (referee)
Title: One factor interest rate models Author: Matúš Jambor Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Petr Myška Abstract: In this thesis we looked closely at the models of interest rates that are applied in the area of financial mathematics and actuarial sciences. There are several models that try to describe the behavior of yield curve plausibly. In most of the cases the models stem from probability theory and coincidence. These models are also means for assessment of financial derivates whose price de- pends on the interest rates movements. The work deals with three one-factor models which are analyzed into more details in the second chapter. The last chapter is about real-data calibration. Keywords: one factor models, interest rates, maximum likelihood method 1
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Applications of EM-algorithm
Komora, Antonín ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
EM algorithm is a very valuable tool in solving statistical problems, where the data presented is incomplete. It is an iterative algorithm, which in its first step estimates the missing data based on the parameter estimate from the last iteration and the given data and it does so by using the conditional expectation. In the second step it uses the maximum likelihood estimation to find the value that maximizes the logarithmic likelihood function and passes it along to the next iteration. This is repeated until the point, where the value increment of the logarithmic likelihood function is small enough to stop the algorithm without significant errors. A very important characteristic of this algorithm is its monotone convergence and that it does so under fairly general conditions. However the convergence itself is not very fast, and therefore at times requires a great number of iterations.
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Hypothesis Testing of interest rates models
Petrík, Daniel ; Myška, Petr (advisor) ; Hurt, Jan (referee)
V předložené práci se zabýváme problematikou stochastického modelování úro- kových sazeb. Jedním z nejobvyklejších postup· je modelovat dynamiku úroko- vých sazeb pomocí stochastické diferenciální rovnice difúze, jejímiž základními kameny jsou funkce driftu a funkce difúze. Od 70. let 20. století byla navržena celá řada model· tohoto typu, a ačkoli se tyto modely neustále zdokonalují, vyvstává přirozená otázka, zda se historicky pozorované úrokové sazby skutečně takovými difúzními rovnicemi řídily. V této práci budeme právě uvedenou hypo- tézu testovat pro několik nejběžnějších jednofaktorových model· úrokové sazby první generace. Z historických dat odhadneme obecnou momentovou metodou a metodou maximální věrohodnosti parametry jednotlivých difúzních rovnic a následně provedeme statistické testy dobré shody proložení těchto rovnic pozo- rovanými daty. 1
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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
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Application of count data models
Reichmanová, Barbora ; Hampel,, David (referee) ; Hübnerová, Zuzana (advisor)
Při analýze dat růstu rostlin v řádku dané délky bychom měli uvažovat jak pravděpodobnost, že semínko zdárně vyroste, tak i náhodný počet semínek, které byly zasety. Proto se v celé práci věnujeme analýze náhodných sum, kde počet nezávisle stejně rozdělených sčítanců je na nich nezávislé náhodné číslo. První část práce věnuje pozornost teoretickému základu, definuje pojem náhodná suma a uvádí vlastnosti, jako jsou číslené míry polohy nebo funkční charakteristiky popisující dané rozdělení. Následně je diskutována metoda odhadu parametrů pomocí maximální věrohodnosti a zobecněné lineární modely. Metoda kvazi-věrohodnosti je též krátce zmíněna. Tato část je ilustrována příklady souvisejícími s výchozím problémem. Poslední kapitola se věnuje aplikaci na reálných datech a následné analýze.
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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 ex-post are calculated optimum model parameters that are used in the ex-ante period, where is calculated performance of the model. The thesis answers question: Are these models gaining from public database effective in modern age?
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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 cross-section 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.
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