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Testing exponentiality
Dvoranová, Romana ; Anděl, Jiří (advisor) ; Hušková, Marie (referee)
This bachelor thesis focuses on detailed review of a selection of tests for exponentiality and their comparison. This text presents classical methods for goodness-of-fit testing for exponentiality, as well as the most recent tests for exponentiality published in the last decades. Based on the characterisation of exponential distribution that is being used, the review includes $\chi^2$ goodness-of-fit tests, tests based on empirical distribution function using Kolmogorov-Smirnov and Cramér-von Misés test statistics, as well as tests based on integral transforms, entropy, mean residual life function, Gini index and others. In particular, this bachelor thesis focuses on tests for exponentiality based on entropy characterisation, e.g. using Shannon, Rényi or cumulative residual entropy. Finally, this thesis includes simulation study comparing power of several more recent tests for exponentiality that have been theoretically described. Powered by TCPDF (www.tcpdf.org)
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Exact envelope tests
Maděřičová, Soňa ; Dvořák, Jiří (advisor) ; Beneš, Viktor (referee)
In this work we are focusing on Monte Carlo simulation tests, in particular we are dealing with envelope and deviation tests. We describe the development of envelope tests from standard envelope tests, in which we can not control significance level, through refined envelope tests, where we can control the significance level indirectly, to exact envelope tests, for which the significance level can be chosen in advance. We will show how the exact envelope tests are related to deviation tests. Further we compare individual kinds of tests using examples and describe their advantages and disadvantages.
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Testing exponentiality
Dvoranová, Romana ; Anděl, Jiří (advisor) ; Hušková, Marie (referee)
This bachelor thesis focuses on detailed review of a selection of tests for exponentiality and their comparison. This text presents classical methods for goodness-of-fit testing for exponentiality, as well as the most recent tests for exponentiality published in the last decades. Based on the characterisation of exponential distribution that is being used, the review includes $\chi^2$ goodness-of-fit tests, tests based on empirical distribution function using Kolmogorov-Smirnov and Cramér-von Misés test statistics, as well as tests based on integral transforms, entropy, mean residual life function, Gini index and others. In particular, this bachelor thesis focuses on tests for exponentiality based on entropy characterisation, e.g. using Shannon, Rényi or cumulative residual entropy. Finally, this thesis includes simulation study comparing power of several more recent tests for exponentiality that have been theoretically described. Powered by TCPDF (www.tcpdf.org)
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Tests for symmetry
Böhmová, Karolína ; Hušková, Marie (advisor) ; Omelka, Marek (referee)
This study deals with testing the hypothesis of univariate symmetry about a known and unknown parametr. In three chapters several nonparametric tests is introduced, which are used to test the hypotesis. Rank tests are first type of tests in this study. It presents basic properties of general rank test of symmetry about a known parametr and well-known rank tests like Wilcoxon test or Van der Waerden test. Next tests based on empirical distribution function are described, specifically test of Kolmogorov-Smirnov type and test of Cramér-von Mises type. Tests based on empirical characteristic function are also described in this study. Finally methods Monte Carlo and bootstrap are used to approximate critical region of same tests. Powered by TCPDF (www.tcpdf.org)
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Decision Problems and Empirical Data; Applications to New Types of Problems
Odintsov, Kirill ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
This thesis concentrates on different approaches of solving decision making problems with an aspect of randomness. The basic methodologies of converting stochastic optimization problems to deterministic optimization problems are described. The proximity of solution of a problem and its empirical counterpart is shown. The empirical counterpart is used when we don't know the distribution of the random elements of the former problem. The distribution with heavy tails, stable distribution and their relationship is described. The stochastic dominance and the possibility of defining problems with stochastic dominance is introduced. The proximity of solution of problem with second order stochastic dominance and the solution of its empirical counterpart is proven. A portfolio management problem with second order stochastic dominance is solved by solving the equivalent empirical problem. Powered by TCPDF (www.tcpdf.org)
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