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Testing heteroscedasticity
Špaková, Mária ; Kalina, Jan (advisor) ; Zichová, Jitka (referee)
Title: Testing heteroscedasticity Author: Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jan Kalina Ph.D., Institute of Computer Science, Academy of Sciences of the Czech Republic Abstract: This paper deals with testing heteroscedasticity. It is divided into four chapters. The first three chapters focus on the theory and the last one is devoted to practical testing using specific data. In the beginning of the theoretical part, basic concepts, knowledge and relationships concerning the linear regression, the regression model and the estimation of parameters by the method of ordinary least squares are introduced. The rest of this part is devoted to heteroskedasticity, its consequences and solutions. The following heteroscedasticity tests are being discussed: Breusch - Pagan, Goldfeld - Quandt and White. The practical part contains actual applications of the described tests and other methods to detect heteroskedasticity using three examples: Outlays vs. income, GDP and Expenditures on food. The aim of this paper is to discuss the above-mentioned tests. Three examples on real data with economic motivation confirm the theoretical properties of the tests. A uniformly optimal test of heteroscedasticity does not exist and different tests yield rather different...
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Parametrizace rozdělení škod v neživotním pojištení
Špaková, Mária ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution.
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Possibilities of using sewage sludge as a secondary source of phosphorus in the Czech Republic.
Václavková, Šárka ; Zach, Boleslav ; Kerberová, V. ; Krejčí, T. ; Krňávek, M. ; Maléř, P. ; Špaková, M. ; Vojtová, I.
A result of the project Possibilities of using sewage sludge as a secondary source of phosphorus in the Czech Republic is a comprehensive study mapping not only the phosphorus content but also the degree of contamination of sewage sludge from various types of wastewater treatment plants in the Czech Republic. This study represents a basis for planning site-specific strategies for the use of phosphorus from sewage sludge in the Czech Republic. Six basic steps led to the elaboration of the study: analysis of the WWTP network in the Czech Republic (1), repeated sampling, analysis of sludge and evaluation of sludge properties of sludges collected from selected facilities representing typical representatives of the nature of source areas and wastewater treatment and sludge treatment technologies (2), legislative analysis of the future of sewage sludge management (3), tests of thermal treatment of sludge and their evaluation (4), search of available technological solutions for sludge treatment (5) and proposal of the concept of sludge treatment in the Czech Republic (6).
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Botanical educational programs for the Bečovská Botanical Garden
ŠPAKOVÁ, Markéta
This thesis is dedicated to educational programs in Bečov Botanic Garden. The aim of this thesis was to extend the current offer to other botanical themes. Dendrological themes were selected for new educational programs. In total, three new educational programs were created. The first one is dealing with conifers, the second with cones of conifers and the third with broad-leaved species. All new programs include worksheets and methodological instruction for lectures and teachers. Tutorial tools (determination key, scale, educational box) were also created for the cone educational program.
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Parametrizace rozdělení škod v neživotním pojištení
Špaková, Mária ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution.
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Testing heteroscedasticity
Špaková, Mária ; Kalina, Jan (advisor) ; Zichová, Jitka (referee)
Title: Testing heteroscedasticity Author: Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jan Kalina Ph.D., Institute of Computer Science, Academy of Sciences of the Czech Republic Abstract: This paper deals with testing heteroscedasticity. It is divided into four chapters. The first three chapters focus on the theory and the last one is devoted to practical testing using specific data. In the beginning of the theoretical part, basic concepts, knowledge and relationships concerning the linear regression, the regression model and the estimation of parameters by the method of ordinary least squares are introduced. The rest of this part is devoted to heteroskedasticity, its consequences and solutions. The following heteroscedasticity tests are being discussed: Breusch - Pagan, Goldfeld - Quandt and White. The practical part contains actual applications of the described tests and other methods to detect heteroskedasticity using three examples: Outlays vs. income, GDP and Expenditures on food. The aim of this paper is to discuss the above-mentioned tests. Three examples on real data with economic motivation confirm the theoretical properties of the tests. A uniformly optimal test of heteroscedasticity does not exist and different tests yield rather different...
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Foundations in Switzerland
Špaková, Martina ; Skovajsa, Marek (advisor) ; Deverová, Lenka (referee)
The aim of this master thesis is to point out the key characteristics of the foundations in Switzerland, to describe their development, underline some specific features and compare them to the foundations in the Czech Republic. Further on, I focus on the systems of quality assurance for foundations and other non-profit organisations, which can be found in Switzerland. Based on their analysis I consider the possibility of implementing of similar systems into the Czech non-profit sector. After the introductory chapter, basic definitions, the history and the typology of the Swiss foundations follow. In the third chapter I describe current legislation concerning foundations and confront it with the laws for foundation in the Czech Republic. Statistical data about the foundations in Switzerland are summed up in the fourth chapter. The next chapter presents the topics of foundation governance and related systems of quality assurance. The existing standards for Swiss non-profit organisations are characterised in the sixth chapter. As a result of previous analysis, in the seventh chapter I summarize some important points for the discussion about using similar systems in the Czech Republic.
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Dendrologic survey of Bečov botanical garden
ŠPAKOVÁ, Markéta
This thesis completes information about the area of the former Beaufort rock garden and contemporary Bečov botanical garden. The main part of this work is dendrologic survey and passport of woody plants in the area. The two parts of the original area were chosen for the survey the former landscape park and the slope with rockery. In total, there were passported 470 woody plants, 104 of them were coniferous and 366 broad-leaved species. There were identified 30 taxa of coniferous in 9 genera and 55 taxa of broad-leaved in 31 genera. All the woody plants were drawn into the plan, which is also part of this work (scale 1:600). Next part of this work is a list of woody plants taxa in the forest complex and the orchard. It was wtitten 34 taxa (3 coniferous and 31 broad-leaved) and 50 varieties of fruit trees.
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Proposal for reconstruction of the historic Beaufort rock garden in the Bečov nad Teplou town (district Karlovy Vary)
ŠPAKOVÁ, Markéta
This thesis will build upon my undergraduate dissertation. It is enriched by the new information about the original historic Beaufort rock garden. It explores the Beaufort rock garden and includes points of view of the experts on its condition today. The following part of the thesis comprises of a proposal for a renewal of the current Bečov botanical garden framework and of a more detailed focus on few selected rocks and their initial planting. The main contribution of this work is an expansion of the total number of the initially grown plants (from 654 to 1228) thanks to the newly found resources and to the writing down all the newly discovered information from the archival research of the original historical documents dated from 1908 to 1937. All the documents were catalogued by the author of the original concept alpina, the head gardener Johann Koditek. What we do know from the original documentation is how the area expanded between the years 1922 - 1927 with the purchase of the surrounding land. It is clear that the expenses for the land were about 18 098,31crowns and for various works, building construction, plants, materials and wages the total sum was 468 336.07 crowns. The exact mounting plans for landscape park were rediscovered (10 plans and inventories in total) and 16 plans and inventories in total of 47 for the rock garden. The chart with the total number of the originally cultivated taxa also consists of the surviving taxa in the area (22 specific herb species + 43 specific tree species and 12 tree genera). The synonymy of the original plants was created for three selected rocks and surveyed their purchase options today. Most of the taxa will return back to the garden, only rock no. 8 will have to be planted differently due to the lack of light on the original plants. Keywords: origin
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