|
|
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
|
|
|
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
|
|
|
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
|
|
|
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...
|
|
|
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
|
|
| |
|
|
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.
|
|
|
The power of two sample tests
Rózsahegyi, Dominik ; Maciak, Matúš (advisor) ; Komárek, Arnošt (referee)
Two-sample tests are one of commonly used statistical tools with which we make decisions if experimentally obtained data from different populations satisfy pre-specified statement. Suitability of using them could be dedicated by the power of test, which states for probability of rejection of invalid statement. The reader gets to know with terms of hypothesis testing which are necessary for introduction of tests. The second chapter introduce tests which could be used when analysed data are complete. If some observations are not exactly known, we call them censored and it is more suitable to use tests listed in the third chapter. We estimate the power for tests in simulations and observe its behavior with different conditions. 1
|
|
|
Distribution of interpoint distances
Horská, Šárka ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
This thesis investigates basic properties of the interpoint distances be- tween random vectors drawn from multinomial distribution. We also describe a possible application to testing sparse observations, i.e., a setup with small number of observations and large number of categories, where the classical χ2 -test cannot be recommended. As an alternative, utilizing the multinomial interpoint distances, we will present the test statistic proposed by Biswas and Ghosh (2014). 1
|
|
|
Analysis of fluctuation of labourers
Zeman, Ondřej ; Maciak, Matúš (advisor) ; Komárek, Arnošt (referee)
The main goal of this thesis is to analyse the fluctuation of the employees in a well established Czech manufacturing company. Due to the GDPR regulations, the underlying company is kept anonymised in this thesis. The data were transformed into longitudinal data and the GEE methodology was used for the analysis of the fluctuation. In the first chapter, an introduction to the problem and a short description of the data is provided. The second chapter contains some theoretical description of the GEE methodology and the QIC information criterion. In the third chapter, multiple models for a binary and multinomial response are fitted to the data and their results are described in detail. This allows us to describe the influence of various factors to the fluctuation of the employees in the underlying company. 1
|
guest ::
RSS feed.