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National Repository of Grey Literature

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Analysis of cross-over clinical trials in the presence of baseline measurements Helebrand, František ; Kulich, Michal (advisor) ; Komárek, Arnošt (referee) This thesis aims to provide a comprehensive overview of methods for estimating treat- ment effects in cross-over designs. It examines approaches that use baseline measurements to estimate the treatment effect, as well as alternative methods that do not use baseline measurements at all. It also proposes new approaches to estimating treatment effects and introduces robust procedures to ensure that biases caused by residual treatment effects from the previous period are within acceptable limits. The theoretical properties of the methods are investigated in a simulation study. Furthermore, a comparison of different methods is performed in cases where a theoretical comparison is not possible. 1 Detailed record

Skew normal distribution Helebrand, František ; Hudecová, Šárka (advisor) ; Antoch, Jaromír (referee) Title: Skew normal distribution Author: František Helebrand Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Šárka Hudecová, Ph.D., Department of probability and mathematical statistics Abstract: In this paper, the skewed normal probability distribution is studied. First, the density is proposed and the basic properties of this distribution are proved. Then the thesis deals with the moment and cumulative generating functions. These functions are used in deriving the mean, variance and skewness of the skew normal distribution. In the third chapter, two parameter estimators are proposed and their properties are derived. Finally, these estimators are empirically investigated in a simulation study and on real data. Keywords: normal distribution, skewness, point estimators 1 Detailed record

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