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Modelování extrémních hodnot
Shykhmanter, Dmytro ; Malá, Ivana (advisor) ; Luknár, Ivan (referee)
Modeling of extreme events is a challenging statistical task. Firstly, there is always a limit number of observations and secondly therefore no experience to back test the result. One way of estimating higher quantiles is to fit one of theoretical distributions to the data and extrapolate to the tail. The shortcoming of this approach is that the estimate of the tail is based on the observations in the center of distribution. Alternative approach to this problem is based on idea to split the data into two sub-populations and model body of the distribution separately from the tail. This methodology is applied to non-life insurance losses, where extremes are particularly important for risk management. Never the less, even this approach is not a conclusive solution of heavy tail modeling. In either case, estimated 99.5% percentiles have such high standard errors, that the their reliability is very low. On the other hand this approach is theoretically valid and deserves to be considered as one of the possible methods of extreme value analysis.
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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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Development of Values of HDI
Svobodová, Veronika ; Malá, Ivana (advisor) ; Helman, Karel (referee)
This bachelor thesis deals with examination and quantification of quality of life defined by the Human Development Index predominantly in European countries. Thesis is divided into three parts. In the first part of this thesis is defined the quality of life and are mentioned reasons of its examination. Further is noted the idea of sustainable development. Second part focuses on its own calculations, especially the description of development of values of the HDI, decomposition of the HDI to its components and comparing the HDI with another economic and demographic indicators. The third part discusses found results, these results are compared with already published research and another sources. In this thesis is also possible to find critical views on the HDI and another ways of measuring the quality of life.
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Mixed Models and Their Application in Medical Data Analysis
Mohammad, Adam ; Malá, Ivana (advisor) ; Bašta, Milan (referee)
This bachelor thesis deals with the description of the linear mixed model. At first, the model is described theoretically and the basic terms, model specification, estimation of unknown parameters, model-building and model diagnostics are explained. In addition, types of data for which the model may be applied are listed and some examples of applications in medicine are given as well. The second part of this thesis deals with the practical application of the model for analysis of longitudinal data from a medical research. The data contain information about 12 patients to whom a drug named theophylline was given and the concentration of this drug in blood was measured within one day. By statistical software R the dependency of the concentration on time, dose and weight of the patient is described. However the results of the analysis show that the dependency of concentration on time cannot be described by a simple function, therefore this dependency has to be described and the data modified prior to application of linear mixed model on data. The other possibility is to use a different model.
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Analýza dat týkajících se risku sebevraždy u mentálně nemocných
Hron, Jiří ; Rauch, Jan (advisor) ; Malá, Ivana (referee)
The three goals of this thesis are to present a coherent overview of the research on suicide in both the general population and among mentally ill, to analyse records of hospitalisations of mentally ill from years 2006 to 2012 while looking for patterns either leading to identification of suicide risk factors or useful for predicting probability of suicide at the time of discharge, and finally to compare a selected subset of statistical, data mining and machine learning methods in relation to their applicability to the second goal. The overview is based on information from over 40 published articles. The analysis and the comparison make use of associative rules mining, visual and stepwise methods for exploration, standard and conditional logistic regression models for inference, and variations of random forests for prediction. To the best of author's knowledge, none of the three goals was previously pursued by any other researcher in the Czech Republic, certainly not using the data set provided for purposes of this thesis. A new modification of random forest combined with a set of logistic regression in order to refine prediction accuracy is also briefly explored. The structure closely follows the above--stated goals starting from the chapters on related work and on the theoretical basis of the methods used, and concluding by the analysis itself and discussion of its results.
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Comparison of life quality in countries of European Union measured by various indicators
Knoll, Radim ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
In this bachelor thesis I try to describe the quality of life using a wider range of components which affects the quality of life and use these components to compare the quality of life in 28 member countries of the European Union. This work is divided into four parts. The first part is a detailed description of individual components of life quality. Along with that a comparison of all indicators of life quality is shown. Compared indicators were used in multiple calculations and models of life quality. The second part contains an overall comparison of the European Union based on all indicators. The third part consists of a comparison of the values of selected indicators in years of 2007 and 2013. Furthermore cluster analysis which is based on similarity of states classified by chosen indicators is shown. The last part contains a list of individual states ranked by the quality of life in years of 2008 and 2012.
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Comparison of the Bayesian and Frequentist Approach to the Statistics
Hakala, Michal ; Karel, Tomáš (advisor) ; Malá, Ivana (referee)
The Thesis deals with introduction to Bayesian statistics and comparing Bayesian approach with frequentist approach to statistics. Bayesian statistics is modern branch of statistics which provides an alternative comprehensive theory to the frequentist approach. Bayesian concepts provides solution for problems not being solvable by frequentist theory. In the thesis are compared definitions, concepts and quality of statistical inference. The main interest is focused on a point estimation, an interval estimation, a statistical hypothesis testing and finally a stochastic convergence. The contribution of the thesis is a brief compilation of the Bayesian theory and introducing new arguments and examples in the discussion between proponents of the Bayesian and frequentist approach to statistics.
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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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Statistical survey of injuries in childhood
Suchopár, Jan ; Malá, Ivana (advisor) ; Sobíšek, Lukáš (referee)
This bachelor thesis deals with the analysis of injuries in childhood. Data we obtained through a questionnaire survey of primary school pupils and pediatric surgeries. Thesis is divided into five parts. The first part describes the causes of injuries. Statistical methods are described in the second part. The third part focuses on methods of data collection and the creation of the questionnaire. The data are processed in the fourth and in the fifth part. The goal is to verify the theory of frequency of injuries in dependence on age, sex and activities of a child using statistical methods. The conclusion summarizes the results of each survey.
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An Analysis of Unemployment in Poland and the Czech Republic
Vavrečková, Klára ; Čabla, Adam (advisor) ; Malá, Ivana (referee)
The subject-matter of this bachelor thesis is an analysis of unemployment in the Czech Republic and Poland with a main focus on long-term unemployment which has a negative effect on an individual as well as on the state's economy. The major goal of this thesis is to compare the development and structure of unemployment in both countries from different perspectives by using appropriate statistical methods. The first part focuses on a clarification of terms such as unemployment. The second part of this paper compares the basic and common characteristics of the countries. The next part is devoted to the theory of the statistical methods which are use in the analytical part. Based on the data taken from Eurostat and the Czech Statistical Office in the year 1998--2013 is in the analytical part used the Analysis of Variance, analysis of trend and forecast of the long-term unemployment by using the exponential smoothing method. The bachelor thesis provides a compact insight into problems of unemployment in the Czech Republic and Poland.
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