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Territorial Differentiation of Elementary Education in Czechia during the 2nd Half of the 20th Century (Its Influence on Local and Regional Development)
Kučerová, Silvie ; Chromý, Pavel (advisor) ; Anděl, Jiří (referee) ; Siwek, Tadeusz (referee)
Územní diferenciace elementárního vzdělávání v Česku v 2. polovině 20. století (Vliv na lokální a regionální rozvoj) Od druhé poloviny 20. století jsme v mnoha hospodářsky vyspělých zemích, Česko nevyjímaje, svědky procesu výrazné polarizace prostoru v souvislosti se změnami v rozmístění elementárních škol. Masové uzavírání škol, zejména na venkově, a koncentrace vzdělávací funkce do center regionů vychází z obecných procesů, jakými jsou změny geografické organizace společnosti, stejně jako ze specifických historických podmínek v každé zemi. V této práci se na příkladu Česka pokusíme představit pomocí metod, jež jsou geografům vlastní, změny, které proběhly v síti elementárních škol. Dále budeme specifikovat vybrané důsledky tohoto procesu na stabilitu a fungování lokálních komunit a jeho vliv na marginalizaci obcí. ABSTRACT Territorial Differentiation of Elementary Education in Czechia during the Second Half of the Twentieth Century (Its Influence on Local and Regional Development) We are all witnesses to a process of extensive spatial polarization in the distribution of elementary schools in many economically developed countries, including Czechia, during the second half of the 20th and in the 21st century. Processes of mass school closures, especially in rural areas, and the concentration of...
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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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Chebyshev inequality and some its modifications
Drabinová, Adéla ; Anděl, Jiří (advisor) ; Nagy, Stanislav (referee)
In the presented thesis we describe some improvements of Chebyshev inequa- lity. In the first chapter we introduce inequalities for random variables with uni- modal distributions. We prove Gauss and Camp-Meidell inequality and we deduce Vysochanskii-Petunin inequality. We describe inequalities for variables with mode 0 and with unspecified mode. In the second chapter we consider constants C(r), for which the approximations are the best. We are interested in finding optimal parameter r or its approximation. In the third chapter we state inequalities from the first chapter for specific distributions, calculation of their constants, appli- cations and graphic presentations of the results. 1
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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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Errors-in-variables models
Fürjesová, Ida ; Pešta, Michal (advisor) ; Anděl, Jiří (referee)
This thesis analyzes an errors-in-variables model. It compares parameter estimation methods least squares and total least squares. The main difference between these methods lies in approach to the measurements errors. The first part of the bachelor thesis focuses on theoretical aspect of methods. It defines basic terms and shows differences in the methods graphically. Thesis also demonstrates algebraic solutions of the estimation methods. The theoretical part ends up with statistical properties of the estimating techniques. The thesis compares methods least squares and total least squares according to the size of mean square error by simulation study.
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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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Nonnegative time series
Ročková, Veronika ; Anděl, Jiří (advisor) ; Štěpán, Josef (referee)
Models for non-negative time series nd their usefulness in many diverse areas of applications (hydrology, medicine, nance). The non-negative nature of the observations has been utilized for deriving estimators with superior asymptotic properties. For the purposes of estimation, it is necessary to recognize the situations when the estimated model indeed de nes a non-negative time series. Such non-negativity conditions can then be used as a basis for constrained optimization. The main thrust of this work is to review the non-negativity conditions currently available for ARMA models and, more importantly, to generalize the existing results for some models for which the explicit result was missing. We center our discussion mainly on univariate models. However, we note that the pursued ideas are directly applicable also for multivariate time series. This observation enables determination of some readily obtainable conditions for lower order vector valued Autoregressive Moving Average models.
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