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Analysis of Properties of Robust Estimates
Sládek, Václav ; Bílková, Diana (advisor) ; Malá, Ivana (referee)
The aim of this thesis is to analyze the properties of robust estimates and to compare these estimates with regard to the properties between them. The analysis of properties depends on the type of a variable (continuous or discrete), its probability distribution, the range of random sample and the proportion of outliers in random sample. Comparing the properties in different situations will give "guidance" to determine which of the estimates is preferable in specific situations, and which of them should be rather avoided. An adjusted bootstrap method is used to obtain the estimates of properties estimates. The thesis is devided into two parts. In the first part, the parameter estimates, type and design of robust estimators and the bootstrap method are monitored. In the second practical part we determine the suitability of bootstrap to obtain estimates of the properties of robust estimators, followed by obtaining estimates of the properties of the estimates and compare them. At the conclusion of the practical part we observe and compare the values of bootstrap confidence intervals on real data on household income. The results of this thesis shows us, that the bootstrap method does not provide good estimates of the properties of robust estimators in all cases. The results also bring us to the conclusion that from a certain extent of random sample regardless of the number of outliers, you can choose from a robust estimate only on the basis of its value, properties of robust estimates are very similar. Contemplated robust estimates of variability are not suitable estimates in most cases.
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Statistical methods in R
Jiráň, Robin ; Löster, Tomáš (advisor) ; Bílková, Diana (referee)
This thesis deals with the most important statistic methods, ways of calculating and syntax in the environment of R statistic programme. The initial parts of the bachelor thesis content a brief theoretical basis for the main chapters of the practical part. In the following chapters the use of R programme itself for calculating statistic tasks is explained. The particular parts of recording functions in R programme are presented, important arguments are described and both text and graphical inputs are displayed.
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Power analysis
Král, Ondřej ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This thesis examines the issues of analysis of statistical power of a test. It introduces a subject of hypotheses testing which is closely related. The goal is to expose the effect of parameters' alteration on the power test size. By using an application on examples, the thesis graphically illustrates the differences caused by the parameters' alteration. The results show how is the power of a test influenced by the effect of type one error, type two error, the number of observations, the formulation of alternative hypothesis and effect size on test power. The thesis further elaborates on effect size forms. In conclusion, all the explained theories are tested by an example that illustrates the size, which is achieved by changing the parameter.
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Assistance services within car insurance and accident insurance
Musilová, Klára ; Bílková, Diana (advisor) ; Makhalova, Elena (referee)
The bachelor thesis is focused on selected companies providing services in the field of roadside assistance in the Czech Republic. It will describe only companies belonging to the Association of Czech assistance companies. Then they will be matched by various factors. The work will be also focused on the current topic of crash hunters. There will be used different statistical methods data relating to assistance services from unnamed assistance company. It will be analyzed by using selected characteristics of descriptive statistics and a one-way analysis of variance. Then will be done the questionnaire survey regarding to assistance services. Respondents will be Czech citizens owning a driver license. Then data obtained by interviews will be evaluated. Some of the findings in the survey will be analyzed by using chi-square test in combination table, due to dependencies on knowledge assistance services from the point of view of clients according to the length of ownership of the driver license.
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Statistical Analysis in Web Environment
Postler, Štěpán ; Löster, Tomáš (advisor) ; Bílková, Diana (referee)
The aim of this thesis is creating a web application that allows dataset import and analyzing data with use of statistical methods. The application uses a user access that allows multiple number of persons manipulate with a single dataset, as well as interact with each other. Data is stored on a remote server and application is accessible from any computer that is connected to the Internet. The application is created in PHP programming language with use of MySQL database system, and user interface is built in HTML language with use of CSS styles. All parts of application are stored on an attached CD in form of text files. In addition to the web application, a part of the thesis is also a text output, which contains a theoretical part in form of description of the chosen statistical analysis methods, and a practical part containing list of application's functions, data model's description and demonstration of data analysis options on specific examples.
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Possible ways of determining value of Life Insurance Company
Zaderlíková, Šárka ; Janeček, Martin (advisor) ; Bílková, Diana (referee)
This thesis is focused on describing chosen methods used in liabilities valuation of Life Insurance Company. This is the basis for a valuation of whole Insurance Company. Next goal is real valuation of liabilities and the whole company. The value of liabilities is computed with the Market Consistent Embedded Value methodology and valuation of the company is expresed with Appraisal Value, which is currently one of the most widely used methods for valuation of a life Insurance Company. The valuation is based on values of a fictious company, but the used insurance portfolio corresponds with real life data. The valuation is computed in pessimistic, middle and optimistic variant of company development. Closing this thesis is a sensitivity analysis of assumptions, influencing value of MCEV, where a change of the costs and commisions proved to be of most significance.
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Unisex premiums in the life insurance
Sklenářová, Markéta ; Bílková, Diana (advisor) ; Löster, Tomáš (referee)
The task of the thesis is to determine the effects of legislative changes in the area of life insurance in force since 21 December 2012. Legislative change concerns approach to calculating premiums for life insurance. According to the new provisions of the previous procedure considered sexually discriminatory and gender effect had to be removed. The thesis is focused on examining the impact of the new approach to actuarial calculations. First introduces the reader to the general features of life insurance premium calculation for the derivation of individual life insurance products and determining the amount of the reserve. The practical examples show how to change premiums and reserves for men and women at different ages. Regression analysis is then examined whether the age of the insured may have an impact on the amount of the reserve. This thesis presents the possible consequences in access regardless of sex as insurance premiums, and especially on the reserve, which is the main component of capital insurance.
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Old age pension
Štěrba, Michal ; Bílková, Diana (advisor) ; Löster, Tomáš (referee)
This thesis explores the ever-current topic of pensions, which are devoted to three different chapters . The first part descriptes history development of old-age pensions, focusing on developments in the last more than 200 years. Emphasis is placed on the development of the territory of the present Czech Republic and for each period are also enclosed a historici fact that not only the development of the pension system determined . Another chapter is devoted to an over view of different types of pension system. Together with a description of each pillar by the World Bank definition are also accompanied by examples of systems from different European countries. The last and most extensive part of the work is to point out the existing demographic development of the czech population, finding appropriate indicators applicable to the issue of pensions, to find the possible future evolution of these indicators using statistical and demographic methods and last but not least the program provides potential candidates for the calculation of future retirement or the age at which a person is able to retire . The work will provide readers with comprehensive information not only on the current state pension insurance in the Czech Republic and in Europe but also can learn about the reasons that led to the establishment of what is possible developments, together with suggestions.
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Calculation of life insurance premium and reinsurance premium
Šištíková, Markéta ; Bílková, Diana (advisor) ; Löster, Tomáš (referee)
This thesis deals with actuarial methods that are used for life insurance and reinsurance, for traditional insurance products (whole life, term insurance, pure endowment, endowment, whole life annuity, temporary annuity). The main goal of this thesis is to outline the actuarial methods used for life insurance premium and reinsurance premium. The work is focused on the comparison of the unisex rates, gender specific rates and legislation changes for both sides, insurance company and policyholder. The model examples for each combination of insurance type and gender specific rates (male, female and unisex) are presented.In the last part of the thesis, the time series of the written premium for the Czech Republic market are analyzed for years from 2006 to 2013. The regression model is used to predict the development in next two years.
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Cluster analysis of European Union states using social and economical indicators
Černý, Andrej ; Löster, Tomáš (advisor) ; Bílková, Diana (referee)
Dissertation follows up cluster analysis of European Union states using social and economical indicators. In the first part all the social and economical indicators are defined. In the second part of the dissertation all these indicators in time of economical and financial and later debt crisis in years from 2007 to 2012 in European Union states are analysed. In the third part the cluster analysis is applicated for the social and economical indicators of the European Union states. Five clusters were identified using cluster analysis. Structure of these clusters was changing during years 2007 and 2012. First cluster contained developed Western European countries (Belgium, Denmark, Germany, Ireland, France, Netherlands, Austria, Finland, Sweden and United Kingdom). The second cluster was created from countries, that entered to European Union after year 2004 (Bulgaria, Estonia, Croatia, Latvia, Lithuania, Hungary, Poland, Romania and Slovakia). The third cluster contained Czech Republic, Estonia, Greece, Lithuania, Portugal, Slovakia and Slovenia. In the fourth cluster were Southern European countries Greece, Spain, Italy, Cyprus and Malta and the fifth cluster contained only Luxembourg.
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