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Extreme value theory
Pelinka, Adam ; Čabla, Adam (advisor) ; Gerthofer, Michal (referee)
Extreme value theory is a modern statistical method for modelling events with a very low probability. During the analysis, we deal with convergence of distribution of these extremal events to their limit distributions. These distributions are generalized extreme value distribution and generalized Pareto distribution, which estimate tails of empirical probability distribution, where extremal events occur. In the last years, extreme value theory is used in many fields of study, e.g. in estimating financial risk or in estimating size of floods. In this work, two methods of modelling extremal events are presented - block maxima method and peaks over threshold method. Both methods are used during the real data analysis of daily discharge of river Vltava and estimated models are summarized. Although both used methods give slightly different results, choice of the appropriate model is not clear.
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Odds betting
Kuruc, Michal ; Čabla, Adam (advisor) ; Malá, Ivana (referee)
This bachelor thesis deals with problematics of odds betting. The goal of this thesis is to inform the reader about betting shops, betting environment and basic hypothesis about how to became a successful person in betting. The other goal is to test selected betting strategies and figure out if it is possible to make long-term profit from odds betting. In the theoretical part I show the probable dysfunction of the roulette strategy called martingale. Then I test selected betting strategies on real football results. The thesis may also be used as some kind of simple manual about how to make betting analysis and getting the results from them. The results of this work show that there is probably no guaranteed way how to make profit from odds betting but I think that this thesis can be used to gain some advantages in the betting environment.
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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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Unemployment Duration in the Czech Republic Through the Lens of Survival Analysis
Čabla, Adam ; Malá, Ivana (advisor) ; Komárková, Lenka (referee) ; Popelka, Jan (referee)
In the presented thesis the aim is to apply methods of survival analysis to the data from the Labour Force Survey, which are interval-censored. With regard to this type of data, I use specific methods designed to handle them, especially Turnbull estimate, weighted log-rank test and the AFT model. Other objective of the work is the design and application of a methodology for creating a model of unemployment duration, depending on the available factors and its interpretation. Other aim is to evaluate evolution of the probability distribution of unemployment duration and last but not least aim is to create more accurate estimate of the tail using extreme value theory. The main benefits of the thesis can include the creation of a methodology for examining the data from the Labour Force Survey based on standard techniques of survival analysis. Since the data are internationally comparable, the methodology is applicable at the level of European Union countries and several others. Another benefit of this work is estimation of the parameters of the generalized Pareto distribution on interval-censored data and creation and comparison of the models of piecewise connected distribution functions with solution of the connection problem. Work brought empirical results, most important of which is the comparison of results from three different data approaches and specific relationship between selected factors and time to find a job or spell of unemployment.
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CHAID and logistic regression
Novák, Jaroslav ; Čabla, Adam (advisor) ; Matějka, Martin (referee)
The aim of this thesis is to introduce logistic regression and method dedicated to construction of decision trees called CHAID, compare these two methods with regard to interpretation of their outputs. In order to accomplish the set goals application of these methods will be presented on real dataset. Statistical software will be used to obtain outputs. The outputs will be interpreted and conclusions on their bases will be presented. This thesis will also introduce possibilities of interpretation of these outputs and pros and cons that are connected with them.
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Survival Analysis in R
Pásztor, Bálint ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
Survival analysis is a statistical discipline that analyzes the time to occurrence of certain events. The aim of this thesis is to describe the possibilities of survival analysis in the environment of statistical software R. Theoretical knowledge is applied to real data, parametric and nonparametric estimates of survival functions are evaluated by different methods and compared with each other. In the section focusing on nonparametric models Kaplan-Meier and Nelson-Aalen functions are described. Among the parametric estimates there were included well-known probability distributions, survival functions and risk functions derived from these distributions are presented and there is discussed their usefulness in survival analysis. Another aim is to show the possibility of deriving transition probabilities from estimates and building a Markov chain model to capture the changes of studied cohort over time. The second part of the work contains a description of the applications of the theory of survival analysis. In this section there are shown possibilities of statistical modeling in the field of survival analysis using the software R. Outputs from R were used to create Markov model. There are presented possibilities of pharmacoeconomic models and description of the basic concepts of HTA. Cost-effectiveness calculations using ICER were conducted in accordance with the methodology of SUKL. It was shown that the statistical modelling of survival plays an important role in the evaluation of the cost-effectiveness of medicines.
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Comparing of length of employment before and during the financial crisis
Vágner, Hubert ; Čabla, Adam (advisor) ; Malá, Ivana (referee)
In this bachelor thesis I introduce survival analysis and distribution of time-to-event. The analyzied subject is the resignation from work. It means that I find out and compare how long on average people had work before the financial recession of 2008-2009 and during the time period of the 2010-2011 recession. The data gathered is from the Labor Force Survey, which is produced by the Czech Statistical Office. I used interval censoring to gather the data for the average length of the working ratio. This means that we know that the observed event happened in a given interval, in this case the intervals are individual survays. First of all, it's necessary to estimate the survival function. We shall do this with the help of the nonparametrical Turnbull's estimate for data in interval censoring. Than we calculate individual averages. The empirical part will consist of individual comparisons of the survival function and the average lengths of the working ratio, first for the overall population, second for separate genders and finally for various education levels.
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CHAID - decision tree construction technique
Freyvald, Michal ; Vild, Jiří (advisor) ; Čabla, Adam (referee)
CHAID analysis (Chi-squared Automated Interaction Detection) is a construction technique of decision trees, which is especially suitable for categorical data and is based on Paerson's chi-square statistical test of independence of categorical fields. Important characteristics of decision trees are summarized and structure of CHAID analysis, particular phases of analysis construction, advantages, disadvantages and recommended settings for a high- quality analysis are described in this paper. On exemplary sample from customers segment we're observing usage of CHAID in practise and with the help of IBM SPSS PASW Statistics v18.0 software we're proving usefulness of CHAID analysis in target marketing.
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Analysis of development of spectator attendance at First football league matches since 1963
Hradilová, Lenka ; Čabla, Adam (advisor) ; Vild, Jiří (referee)
In modern society there are a lot of types of entertainment and ways to spend leisure time. Very popular type of entertainment is sport. The attractiveness of each sport is changing in time a lot. The aim of this work is to analyze the attractiveness of football, which is measured by the average number of viewers. At first,work will be focus on the evaluation of the average attendance at First football league matches since 1963. Then an average spectators attendance of three famous football clubs is analyzed in more detail. The last part is devoted to examining the dependence of the average number of viewers for each team on the success of the team measured by the number of points obtained in the relevant season.
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Statistical hypothesis testing using sports data
Černý, Jakub ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
This bachelor thesis is based on empirical study of betting odds of six world-wide betting offices. Using statistical hypothesis testing it tests similarity among offices predictions of five best football leagues and whether the predictions correspond with final results of these games. It has been demonstrated that betting offices predict matches identically but predictions does not correspond with final results. In the second part of this paper, the betting offices are experimentally treated as bettors and their return on investment is monitored. From the comparison of returns and mean squared error of predictions, betting offices Bet365 and BetVictor can be considered as those with the best predictions. Analysis of Fortel servis betting diary has shown that using betting advisory service can lead to long-term profits. It is a proof that betting offices can be beaten over a long time which was also one of the objectives of this paper.
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