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Limited and censored explained variables
Kostka, Rudolf ; Bejda, Přemysl (advisor) ; Komárek, Arnošt (referee)
In this thesis at first we focus on theory of dealing with limited and censored explained variables. We begin with discrete variables and show the theory of binary and categorical variables. Later we explain utility of models logit and probit and demonstrate it at a practical example. We also provide a comparison of these two models. Third chapter deals with limited explained variables, specifically censored, truncated and variables representing some time to event. In the last chapter we describe some functions, which might be used to plot a graph of a survival function using softwares R or Mathematica. Some options in Excel are also mentioned, but they are very limited. Described functions are then demonstrated in use at a practical example with our gained data. Powered by TCPDF (www.tcpdf.org)
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Profitability of life policies and compound GLM
Kostka, Ján ; Pešta, Michal (advisor) ; Komárek, Arnošt (referee)
Life insurance policies are not equally profitable is sense of expected value. In practice, profitability is an output of complex cash flow models, which need utilizing special systems and the run time of such calculation can be significant if number of policies is high. Therefore we consider variables, which change most frequently, stimulate the profitability model with several values of these variables and then we search for a regression model to explain the changes. We apply Gamma regression on the data. But what if there exist some policies which are negative? Then we determine these policies with logistic regression applied on data censored to the binary form. Loss of these policies is modelled using symmetrical Gamma model. These three models, when considered together, can be viewed as a single model, which is a generalization of the well known zero inflated count model. The most interesting part of inference in such model is diagnostics. We show that the basic types of residuals - Pearson, deviance and quantile - can be defined. We also build an ordinary linear model and we compare utility of these two approaches. While building models, we meet various statistical issues like dimension reduction of yield curve or dispersion proportional to sum insured. 1
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Applications of Bayesian Model Selection
Macek, Tomáš ; Večeř, Jan (advisor) ; Komárek, Arnošt (referee)
The Thesis deals with Bayesian model selection. In the theoretical part, readers will get to know with the priciple of Bayesian approach and the Thesis also states Bayes theorem, which has a key role in the given problematics. Next, it elucidates possibilities of choosing prior distribution and introduces Bayesian regression model, especially Zellner's method, which can be used to choose the most suitable model. In the practical part, this method is then implemented using R on real data from English Premier League football matches. From several statistics considered, the method will select the most suitable model, which means that it will select those statistics which are the most important for the match outcome. 1
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Multivariate Extensions of Poisson Distribution
Růžička, Tomáš ; Komárek, Arnošt (advisor) ; Pawlas, Zbyněk (referee)
In this bachelor thesis we introduce several models of multivariate Poisson distribu- tion. At first we briefly mention univariate Poisson distribution and prove subsidiary theorem. We further introduce two models, which rely on properties of the univariate Poisson distribution. The second chapter is supplemented by proven theorems, which deal mainly with the calculation of probability. In the next chapter are proposed point estimators of the model parameters and derived their properties. Finally we demonstrate numerical calculation and three simulations. The last chapter summarizes some other models of multivariate Poisson distribution. 1
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Detection of causality in time series using extreme values
Bodík, Juraj ; Pawlas, Zbyněk (advisor) ; Komárek, Arnošt (referee)
Juraj Bodík Abstract This thesis is dealing with the following problem: Let us have two stationary time series with heavy- tailed marginal distributions. We want to detect whether they have a causal relation, i.e. if a change in one of them causes a change in the other. The question of distinguishing between causality and correlation is essential in many different science fields. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. In this thesis, we propose a new method that can help us in such a nontraditional case distinguish between correlation and causality. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between different time series. We will rigorously prove this claim, and we also propose a method on how to statistically estimate the causal tail coefficient from a finite number of data. The advantage is that this method works even if nonlinear relations and common ancestors are present. Moreover, we will mention how our method can help detect a time delay between the two time series. We will show how our method performs on some simulations. Finally, we will show on a real dataset how this method works, discussing a cause of...
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Lilliefors test of normality
Macoun, Jaromír ; Komárek, Arnošt (advisor) ; Maciak, Matúš (referee)
In this bachelor thesis will be shown one-sample Kolmogorov-Smirnov test, which compares empirical distribution function with one specified distribution function. At first we introduce marking and prove some basic properties about the test statistics and derive asymptotic critical values for the test. At the end of the first chapter we show consistency of the test. In the next step we initiate Lilliefors test of normality. The crucial outcome of the thesis is that distribution of test statistics with some assumptions is independent of unknown parameters. Finally we show a table of approximated critical values and compare with already publicated. 1
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Regression analysis of current status data
Filipová, Anna ; Kulich, Michal (advisor) ; Komárek, Arnošt (referee)
Survival analysis often includes dealing with data that are censored. This thesis focuses on censoring in the form of current status data. We discuss seve- ral methods of regression analysis of current status data and focus mainly on a method that assumes that the time to event follows the additive hazards mo- del. Under the assumption of proportional hazards for the monitoring time, this method does not require knowing the baseline hazard function and allows us to use the theory and software which were developed for Cox model. We also pre- sent a modification of this method, a two-step estimator, and show that it is asymptotically normal and has the advantage of lower asymptotic variance.
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