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A study of applying copulas in data mining
Ščavnický, Martin ; Holeňa, Martin (advisor) ; Hauzar, David (referee)
Title: A study of applying copulas in data mining Author: Martin Ščavnický Department: Department of Theoretical Computer Science and Mathe- matical Logic Supervisor: RNDr. Ing. Martin Holeňa CSc., Department of Theoretical Computer Science and Mathematical Logic Abstract: Copulas are functions that describe the relationship between a multivariate distribution function and its marginals. They provide a way to model multivariate distribution functions, and are extensively used in finance and studied in data mining. In practice, there are many different copula families and no standard way for choosing the right one. In our work, we compare suitability of different copula families in data mining. We fit classification data using 8 copula families and compare them using 3 mea- sures of fit. We also use a classification algorithm based on copulas and compare its accuracy for different copula families. The results indicate that elliptical copulas fit our data better, but hierarchical Archimedean copulas give comparable accuracy in the classification. We also propose and test a modified method for modelling data using hierarchical Archimedean copu- las, which fits some datasets with negative dependence between attributes better. Based on this modified method, we propose a visualization of depen- dence in data and observe...
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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
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Analysis of incidence of competting risks and application of copula models
Hujer, Peter ; Volf, Petr (advisor) ; Dvořák, Jiří (referee)
This thesis first introduces the basic notions of univariate survival analysis. Then the survival analysis setting is extended to competing risk models, i.e. the cases considering several events of interest or several causes of one event. In the competing risk model, we discuss the problem of identification, which means that it is not possible to identify marginal distributions from observed competing risk data. Next, we present copula models, which are a suitable mathematical tool for modelling dependence structure between random variables. We explain their basic characteristics, present some useful copula families and the relationship of copula parameters with certain dependence (correlation) measures. Further, we show the utilization of copulas within competing risks models and how they can be helpful in the solution of identifiability problem. Finally, we apply the listed theoretical knowledge in a simulated example. Powered by TCPDF (www.tcpdf.org)
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Modelling mortality by causes of death
Valter, Boris ; Mazurová, Lucie (advisor) ; Hurt, Jan (referee)
The aim of this thesis is to provide an overview of methods used in cause-of-death mortality analysis and to demonstrate the application on real data. In Chapter 1 we present the continuous model based on the force of mortality and review the approach using copula functions. In Chapter 2 we focus on the multinomial logit model formulated for cause-specific mortality data, discuss life tables construction and derive life expectancy. In Chapter 3 we apply the multinomial logit model on the data from Czech Statistical Office. We identify the regression model, check its assumptions, present the outputs including the fitted life expectancy, and predicted mortality rates. Later in Chapter 3 we consider several stress scenarios in order to demonstrate the impact of shocked mortality rates on the life expectancy. In Chapter 4 we apply copula functions according to the methodology covered in Chapter 1 and consider cause-elimination stress scenario.
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Multivariate claim numbers models
Zušťáková, Lucie ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
Multidimensional frequency models can be used for modeling number of claims from different branches which are somehow dependent on each other. As in the one-dimensional case Poisson distribution and negative binomial distribution are primarily used for modeling multidimensional claim counts data, only they are extended to higher dimensions. The generalization of multi- dimensional distributions is often done using so-called shock variables, where one random variable is included in all dimensions of a random vector which models claim counts. The more comprehensive approach to modeling dependence uses copulas. Comparison of these models is done on a simulated data of number of claims from two different car insurance guarantees.
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Modelling mortality by causes of death
Valter, Boris ; Mazurová, Lucie (advisor) ; Hurt, Jan (referee)
The aim of this thesis is to provide an overview of methods used in cause-of-death mortality analysis and to demonstrate the application on real data. In Chapter 1 we present the continuous model based on the force of mortality and review the approach using copula functions. In Chapter 2 we focus on the multinomial logit model formulated for cause-specific mortality data, discuss life tables construction and derive life expectancy. In Chapter 3 we apply the multinomial logit model on the data from Czech Statistical Office. We identify the regression model, check its assumptions, present the outputs including the fitted life expectancy, and predicted mortality rates. Later in Chapter 3 we consider several stress scenarios in order to demonstrate the impact of shocked mortality rates on the life expectancy.
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Financial risks with copulas
Prelecová, Natália ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The aim of this thesis is the thorough description of the copula theory. It deals with the theory's basic definitions, classes and characteristics. In addition, relations between copulas and dependence measures are explained. Furthermore, we evaluate the possibilities of copula's parametres estimation and selecting the right copula for real data. Then, the copula theory is interconnected with the basic risk measures in finance. We describe the elementary categorization of financial risks and standard risk measurement approaches. We also define basic risk measures with the emphasis on value at risk. Lastly, we present a real data case study of a selected portfolio.
|
|
|
Analysis of incidence of competting risks and application of copula models
Hujer, Peter ; Volf, Petr (advisor) ; Dvořák, Jiří (referee)
This thesis first introduces the basic notions of univariate survival analysis. Then the survival analysis setting is extended to competing risk models, i.e. the cases considering several events of interest or several causes of one event. In the competing risk model, we discuss the problem of identification, which means that it is not possible to identify marginal distributions from observed competing risk data. Next, we present copula models, which are a suitable mathematical tool for modelling dependence structure between random variables. We explain their basic characteristics, present some useful copula families and the relationship of copula parameters with certain dependence (correlation) measures. Further, we show the utilization of copulas within competing risks models and how they can be helpful in the solution of identifiability problem. Finally, we apply the listed theoretical knowledge in a simulated example. Powered by TCPDF (www.tcpdf.org)
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A study of applying copulas in data mining
Ščavnický, Martin ; Holeňa, Martin (advisor) ; Hauzar, David (referee)
Title: A study of applying copulas in data mining Author: Martin Ščavnický Department: Department of Theoretical Computer Science and Mathe- matical Logic Supervisor: RNDr. Ing. Martin Holeňa CSc., Department of Theoretical Computer Science and Mathematical Logic Abstract: Copulas are functions that describe the relationship between a multivariate distribution function and its marginals. They provide a way to model multivariate distribution functions, and are extensively used in finance and studied in data mining. In practice, there are many different copula families and no standard way for choosing the right one. In our work, we compare suitability of different copula families in data mining. We fit classification data using 8 copula families and compare them using 3 mea- sures of fit. We also use a classification algorithm based on copulas and compare its accuracy for different copula families. The results indicate that elliptical copulas fit our data better, but hierarchical Archimedean copulas give comparable accuracy in the classification. We also propose and test a modified method for modelling data using hierarchical Archimedean copu- las, which fits some datasets with negative dependence between attributes better. Based on this modified method, we propose a visualization of depen- dence in data and observe...
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