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Investigation of dependence of the housing characteristics and the amenities in the dwelling on the household type
Čapková, Kateřina ; Řezanková, Hana (advisor) ; Löster, Tomáš (referee)
The aim of the diploma thesis is to provide a comprehensive overview regarding survey of income and living conditions of households in the Czech Republic and propose a feasible approach to the exploitation of the collected data. The diploma thesis describes the framework of the EU-SILC survey and presents its practical implementation in the Czech Republic. A technique utilizing contingency table analysis is proposed for studying asymmetric relationships between selected housing characteristics and amenities in the dwelling with respect to different household types. The analysis is based on the relative frequencies of housing characteristics observed for particular types of households. The frequencies stem from the sample survey of income and living conditions of households carried out in the Czech Republic under the official title of Living Conditions 2008. Asymmetric measures of association for nominal and ordinal variables were used for the description of the relationships as the examined housing characteristics and household types have the character of alternative, nominal or ordinal variables. The analyses show significant relationship of the selected housing characteristics and the amenities in the dwelling on the monitored types of households.
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Extreme Value Theory in Operational Risk Management
Vojtěch, Jan ; Kahounová, Jana (advisor) ; Řezanková, Hana (referee) ; Orsáková, Martina (referee)
Currently, financial institutions are supposed to analyze and quantify a new type of banking risk, known as operational risk. Financial institutions are exposed to this risk in their everyday activities. The main objective of this work is to construct an acceptable statistical model of capital requirement computation. Such a model must respect specificity of losses arising from operational risk events. The fundamental task is represented by searching for a suitable distribution, which describes the probabilistic behavior of losses arising from this type of risk. There is a strong utilization of the Pickands-Balkema-de Haan theorem used in extreme value theory. Roughly speaking, distribution of a random variable exceeding a given high threshold, converges in distribution to generalized Pareto distribution. The theorem is subsequently used in estimating the high percentile from a simulated distribution. The simulated distribution is considered to be a compound model for the aggregate loss random variable. It is constructed as a combination of frequency distribution for the number of losses random variable and the so-called severity distribution for individual loss random variable. The proposed model is then used to estimate a fi -nal quantile, which represents a searched amount of capital requirement. This capital requirement is constituted as the amount of funds the bank is supposed to retain, in order to make up for the projected lack of funds. There is a given probability the capital charge will be exceeded, which is commonly quite small. Although a combination of some frequency distribution and some severity distribution is the common way to deal with the described problem, the final application is often considered to be problematic. Generally, there are some combinations for severity distribution of two or three, for instance, lognormal distributions with different location and scale parameters. Models like these usually do not have any theoretical background and in particular, the connecting of distribution functions has not been conducted in the proper way. In this work, we will deal with both problems. In addition, there is a derivation of maximum likelihood estimates of lognormal distribution for which hold F_LN(u) = p, where u and p is given. The results achieved can be used in the everyday practices of financial institutions for operational risks quantification. In addition, they can be used for the analysis of a variety of sample data with so-called heavy tails, where standard distributions do not offer any help. As an integral part of this work, a CD with source code of each function used in the model is included. All of these functions were created in statistical programming language, in S-PLUS software. In the fourth annex, there is the complete description of each function and its purpose and general syntax for a possible usage in solving different kinds of problems.
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New Developments in Fuzzy Cluster Analysis
Řezanková, H. ; Húsek, Dušan
The paper deals with a special class of cluster analysis methods where a membership degree is calculated for each object and each cluster. These methods are investigated under the name fuzzy cluster analysis. We present some emerging topics in this area, such as relation fuzzy clustering, soft clusters ensembles, similarity of fuzzy clusters, visualization of clustering results, simultaneous clustering and feature discrimination, and techniques for cluster number determination. Some tasks are illustrated by clustering of binary variables.
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Determination of the Optimal Number of Clusters in Statistical Software Systems
Řezanková, H. ; Húsek, Dušan
The paper deals with approaches to determination of the optimal number of groups of objects which are implemented in clustering algorithms in commercial statistical software packages. Some of these approaches are applied to the example of finding groups of deputies of the Russian parliament on the base of roll-call votes in 2004. The capabilities of software packages S-PLUS, SAS, SPSS, and SYSTAT are described.
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Metody pro stanovení počtu shluků ve statistických programových systémech
Řezanková, H. ; Húsek, Dušan
The paper deals with approaches to determination of the optimal number of groups of objects when objects are clustered by different methods implemented in commercial statistical software packages. These approaches are applied to the example of finding groups of deputies of the Russian parliament on the base of roll-call votes in 2004. The capabilities of software packages S-PLUS, SAS, SPSS, and SYSTAT are compared.
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