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Sensitivity of the chi-squared goodness-of-fit tests to the choice of classes
Kubelka, Vít ; Anděl, Jiří (advisor) ; Antoch, Jaromír (referee)
The chi-squared goodness-of-fit test depends on the choice of classes. It is the purpose of this thesis to investigate differences between p-values depending on the choice of classes in the case of Poisson distribution. Samples from Poisson distribution of various sizes are simulated. For all choices of classes which satisfy condition of minimal theoretical frequency p-value is calculated. The simulations are made for various minimal theoretical frequencies. The unknown parameter is estimated both by modified method of minimum chi-squared and by sample mean. The simulations show that the condition of minimal theoretical frequency of classes is not sufficient and the tests are unreliable. Therefore the rule of almost equal theoretical frequencies in all classes is added and in the further simulation a substantial improvement of the test is shown when this condition is satisfied. Powered by TCPDF (www.tcpdf.org)
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The CDU/CSU share on German Energiewende
Anděl, Jiří ; Nigrin, Tomáš (advisor) ; Mlsna, Petr (referee)
ANDĚL, Jiří: Podíl CDU/CSU na vzniku německé Energiewende. Praha 2015. 32 s. Bakalářská práce (Bc.). Univerzita Karlova, Fakulta sociálních věd, Institut mezinárodních studií. Katedra německých a rakouských studií. Vedoucí práce PhDr. Tomáš Nigrin, Ph.D. Abstract A wide range of changes in the German energy sector, known under the name Energiewende, is associated primarily with the government of the Red-Green Coalition ruling in the period 1998 - 2005. Although the then government of the Social Democrats and the Greens introduced the whole concept, the centre-right government of Helmut Kohl, the predecessor of the Red-Green Coalition and the government of Angela Merkel in the years 2009 - 2013, helped significantly to implement Energiewende. The thesis is focused mainly on 3 factors with which the government of H. Kohl and A. Merkel contributed to the implementation of Energiewende. It is the introduction of the Act on the promotion of renewable energy sources from 1991, the climate policy of H. Kohl and the nuclear phase out of A. Merkel from 2011. The thesis also examines the relevance of the aforementioned steps in relation to the whole energy concept. The next part of the thesis is devoted to the analysis of possible motives that could have influenced the individual steps. As far as the importance is...
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Confidence intervals for parameters of multinomial distribution
Bárnetová, Kamila ; Anděl, Jiří (advisor) ; Omelka, Marek (referee)
Title: Confidence intervals for parameters of multinomial distribution Author: Kamila Bárnetová Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jiří Anděl, DrSc., Department of Probability and Mathematical Statistics Abstract: Confidence intervals for parameters for binomial and multinomial distribution are described in this thesis. These intervals can be used in practice, for exemple- pre-election estimates. The first two chapter are devoted to derivation of these intervals. Simulations and comparison of several selected methods can be found in the last chapter. Based on the simulations, we consider it appropriate, to choose to calculate confidence intervals for parameters of multinomial distribution intervals based on Bonferroniho inequality, or their modifications. These intervals are easy to calculate, while their coverage probability is at least 0.89. Keywords: confidence interval, multinomial distribution, binomial distribution, Bonferroni inequality
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Data fusion
Janíková, Veronika ; Hovorka, Tomáš (advisor) ; Anděl, Jiří (referee)
This bachelor's thesis deals with a data fusion, which is a one of the possible solutions to the common problem of data availability in praxis. In the first part, practical use of data fusion, especially in marketing, fundamental algorithms and data fusion problems are discussed. The main part of this thesis deals with the so-called "unconstrained statistical fusion". Firstly, one of the possible processes of this type of fusion is described theoretically in detail. This process involves branching into four different types of data fusion. Next, a method of theoretical evaluating the quality of the general fusion model is designed using statistical indicators. The practical part of the thesis contents processes of four types of unconstrained statistical fusion and their evaluation which both are programmed in statistical program R. Furthermore, the fusion is applied to our artificially generated database and also to a real data collected in praxis by Czech public opinion research company Median. In the very last part of the thesis, the results of fusions applied to these two databases are interpreted, evaluated and discussed.
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Effects and consequences of turistifacion in Teplice
Čáslavová, Eva ; Fialová, Dana (advisor) ; Anděl, Jiří (referee)
This diploma thesis deals with effects and consequences of touristification in the spa town of Teplice. The aim of this work is the analysis of current state of Teplice's spa therapy and monitoring of functional changes in the town. The emphasis is placed on activities, relational links and the level of co- operation and attitudes of the main participants in the tourism in the town. An inseparable part is also an opinion poll (investigation) among local residents. The aim of this dissertation is, except for findings and an evaluation of effects of touristification in the area of interest, also the suggestion of steps leading to stabilization and improvement of the situation. Powered by TCPDF (www.tcpdf.org)
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Outliers
Kudrnáč, Vojtěch ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
This paper concerns itself with the methods of identifying outliers in an otherwise normally distributed data set. Several significant tests and criteria designed for this purpose are described here, Peirce's criterion, Chauvenet's criterion, Grubbs' test, Dixon's test and Cochran's test. Deriving of the tests and criteria is indicated and finally the results of the use of the test and criteria on simulated data with normal distribution and inserted outlier are looked into. Codes in programming language R with the implementation of these test and criteria using existing functions are included. Powered by TCPDF (www.tcpdf.org)
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Durbin-Watson test
Lipták, Patrik ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
The Bachelor Thesis deals with Durbin-Watson test which is used to test an inde- pendence of residuals in a normal linear regression model. The test is applicable in a case of collecting data gradually and if values of a dependent variable form time series. In the first part, thesis provides detailed derivation of a distribution of test statistic (or its bounds), as well as conclusion describing how to make a right decision in testing a hypothesis that the value of correlation coefficient is equal to 0. In the second part, three practical examples with real data are used to demonstrate this theoretical basis. Moreover, calculations are supplemented by illustrative graphs and they are made in computing environment R for com- parison. 1
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Random triangles
Matula, Dominik ; Anděl, Jiří (advisor) ; Dvořák, Jiří (referee)
The author summarizes some previous results concerning random triangles. He describes the Gaussian triangle and random triangles whose vertices lie in a unit n-dimensional ball, in a rectangle or in a general bounded convex set. In the second part, the author deals with an inscribed triangle in a triangle - let ABC be an equilateral triangle and let M, N, O be three points, each laying on one side of the ABC. We call MNO inscribed triangle (in an equi- laterral triangle). The median triangle is a special case of that triangle. Author starts with the median triangle and one by one replaces it's vertices by random points with uniform distribution on the corresponding sides. He proves that propability of such inscribed triangle to be an obtuse triangle increases with number of randomly chosen points while the expected area reminds constant. The whole thesis is concluded with a simulation study. 1
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Multiple Testing Problem
Waczulík, Oliver ; Komárek, Arnošt (advisor) ; Anděl, Jiří (referee)
Title: Multiple Testing Problem Author: Oliver Waczulík Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek, Ph.D., Department of Probability and Mat- hematical Statistics Abstract: This thesis looks into the different approaches to control the type-1 error inflation, more specifically, it looks into different procedures that control familywise error rate (FWER), when testing more than one elementary hypothesis simultaneously. It focuses on two basic types of problems: comparing the mean of more than one independently normally distributed random sample with the control and com- paring the means of more than one independently normally distributed random sample between each other. To further illustrate the mechanics of the multiple comparison procedures stated in this thesis we use a real measurements of the brain volume of four independent groups of males, where we anticipate normal distribution with the same variance. Global null hypothesis is always tested as first, followed by testing of elementary hypothesis in the case of rejection. To tackle the first problem, we use Bonfferoni and Holm multiple comparison pro- cedures along with Dunnett method and closure principle. Unlike Dunnett with Bonfferoni, Holm and Bonfferoni's closed test provide different conclusion...
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