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Graphical methods for directional data
Tyuleneva, Anastasia ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
Title: Graphical methods for directional data Author: Anastasia Tyuleneva Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: This work is focused on the improvement of knowledge about the graphical directional data visualizing using different kinds of boxplot. The method and restrictions of the boxplot construction are depicted in this work, especially the need of knowledge of the relationship of sample α−quantiles to the theoretical quantiles. The first part is focused on the most importat information of the theoretical background, boxplot and its parts description. In the second part the construction of the circular boxplot for two-dimensional directional data and representation of their properties using von Mises distribution is described. The final part is consisted of a brief description of the method of construction of multidimensional boxplot or bagplot for three-dimensional Fisher distribution. Keywords: boxplot, bagplot, directional data, von Mises distribution, Fisher distribution
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Statistics of directional data with an application in crystallography
Karafiátová, Iva ; Šedivý, Ondřej (advisor) ; Hlubinka, Daniel (referee)
The main purpose of this thesis is to derive methods used to estimate the mean orientation of a grain in polycrystalline material. The estimation is highly impor- tant in crystallography. However, it is often expressed by only one representative value regardless of its variability within the grain. In this thesis we present the basic concepts of crystallography, including the principle of the Electron Backs- catter Diffraction, which is used to explore the microstructure of a polycrystalline materials. Subsequently, we present six of the most commonly used descriptors of three-dimensional orientation of a crystal lattice. This overview is completed by the summary of the particular relationships between those descriptors. In the practical part of this thesis we apply derived methods on real data within the scope of research of microstructure of an aluminum alloy. 1
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Graphical methods for directional data
Tyuleneva, Anastasia ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
Title: Graphical methods for directional data Author: Anastasia Tyuleneva Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: This work is focused on the improvement of knowledge about the graphical directional data visualizing using different kinds of boxplot. The method and restrictions of the boxplot construction are depicted in this work, especially the need of knowledge of the relationship of sample α−quantiles to the theoretical quantiles. The first part is focused on the most importat information of the theoretical background, boxplot and its parts description. In the second part the construction of the circular boxplot for two-dimensional directional data and representation of their properties using von Mises distribution is described. The final part is consisted of a brief description of the method of construction of multidimensional boxplot or bagplot for three-dimensional Fisher distribution. Keywords: boxplot, bagplot, directional data, von Mises distribution, Fisher distribution
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Graphical methods for directional data
Tyuleneva, Anastasia ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
Title: Graphical methods for directional data Author: Anastasia Tyuleneva Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: This work is focused on the improvement of knowledge about the graphical directional data visualizing using different kinds of boxplot. The method and restrictions of the boxplot construction are depicted in this work, especially the need of knowledge of the relationship of sample α−quantiles to the theoretical quantiles. The first part is focused on the most importat information of the theoretical background, boxplot and its parts description. In the second part the construction of the circular boxplot for two-dimensional directional data and representation of their properties using von Mises distribution is described. The final part is consisted of a brief description of the method of construction of multidimensional boxplot or bagplot for three-dimensional Fisher distribution. Keywords: boxplot, bagplot, directional data, von Mises distribution, Fisher distribution
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