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Statistical analysis of data from routing problems
Mazlová, Lenka ; Popela, Pavel (referee) ; Šomplák, Radovan (advisor)
This bachelor thesis focuses on statistical analysis of data retrieved from real waste collection. The main goal is to become familiar with statistical hypothesis testing and model creating typical for mathematical statistics and to determine key parameters that affect routing problems. One of the outputs of this thesis is a Microsoft Excel file that contains statistical tests described in following text.
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Influence of socio-economic factors on the composition of waste: statistical approach
Jordánová, Petra ; Pavlas, Martin (referee) ; Šomplák, Radovan (advisor)
This bachelor thesis deals with comparison of mixed municipal waste in different areas in the Czech Republic. Statistical apparatus needed for subsequent data is described in the first part. There is discussed problematics of random variable, the probability distribution and hypotheses that will be used in this work. The second part involves a data set analysis. The merit of this thesis is hypothesis testing of the difference in mixed municipal waste composition between chosen areas and built-up area types. At the end an approach for estimate of impact factors of waste composition using correlation and regression analysis will be given. This work brings a benefit in current stratification evaluation process and recommendation of changes in selected factors.
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Testing equality of means by confidence intervals
Jandl, Vojtěch ; Kulich, Michal (advisor) ; Pešta, Michal (referee)
We deal with testing the equality of means using confidence intervals. Firstly, we introduce the methods of testing that have already been published. The advantage of these methods is that one can present the underlying confidence intervals alongside the result of the test without doing further calculations. In the second part we discuss the necessary assumptions and by that we extend the Noguchi's method to discrete distribu- tions. Also, we derive a generalization of the Noguchi's method for testing the equality of other parameters than means, based on the assumption of asymptotic normality of their consistent estimates. Lastly, we conduct a simulation study in order to compare the methods we discussed. We found out that the Noguchi's method is a worthy alternative to the often-used Welch test bearing the advantage of being able to present extra visual output in the form of the underlying confidence intervals. In comparison to other methods the Noguchi's method yields better results in the case of unequal or small sample sizes. Unlike other methods it can also be used for testing in the paired sample case. 1
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Visual statistical inference
Jeliga, Jan ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Graphs, and data visualization in general, play a important role in modern statistics. In this thesis, we address the possibility of using these for hypothesis testing. First, we introduce the concept of visual testing and define analogies for terms such as statistic or p-value and additionally we define the terms specific to visual testing. We demonstrate the method of visual testing on an example, where we parallelly perform a conventional test for the same data set and the same null and alternative hypothesis. Further, we inspect the possibility of use of Amazon Mechanical Turk for visual testing. We describe the design of visual test and present results of simulation experiments conducted in order to assess the power of the visual test and to compare it to conventional test. Powered by TCPDF (www.tcpdf.org)
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Testing Structural Changes Using Ratio Type Statistics
Peštová, Barbora ; Hušková, Marie (advisor) ; Prášková, Zuzana (referee) ; Jarušková, Daniela (referee)
Testing Structural Changes Using Ratio Type Statistics Barbora Peštová Charles University in Prague, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Czech Republic Abstract of the doctoral thesis We deal with sequences of observations that are naturally ordered in time and assume various underlying stochastic models. These models are parametric and some of the parameters are possibly subject to change at some unknown time point. The main goal of this thesis is to test whether such an unknown change has occurred or not. The core of the change point methods presented here is in ratio type statistics based on maxima of cumulative sums. Firstly, an overview of thesis' starting points is given. Then we focus on methods for detecting a gradual change in mean. Consequently, procedures for detection of an abrupt change in mean are generalized by considering a score function. We explore the possibility of applying the bootstrap methods for obtaining critical values, while disturbances of the change point model are considered as weakly dependent. Procedures for detection of changes in parameters of linear regression models are shown as well and a permutation version of the test is derived. Then, a related problem of testing a change in autoregression parameter is studied....
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Statistical tests for VaR and CVaR
Mirtes, Lukáš ; Pešta, Michal (advisor) ; Večeř, Jan (referee)
The thesis presents test statistics of Value-at-Risk and Conditional Value-at-Risk. The reader is familiar with basic nonparametric estimators and their asymptotic distributions. Tests of accuracy of Value-at- Risk are explained and asymptotic test of Conditional Value-at-Risk is derived. The thesis is concluded by process of backtesting of Value-at-Risk model using real data and computing statistical power and probability of Type I error for selected tests. Powered by TCPDF (www.tcpdf.org)
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Permutation Tests of Statistical Hypotheses
Veselý, Zdeněk ; Jurečková, Jana (advisor) ; Jarušková, Daniela (referee)
Title: Permutation Tests of Statistical Hypotheses Author: Zdeněk Veselý Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jana Jurečková DrSc., Department of Probability and Mathematical Statistics Abstract: This thesis presents permutation tests concept. Permutation test is demonstrated as response to testing problems where it is inconvenient to make any deeper presumptions on data probability distribution. For some of these problems it is even the only exact solution. The construction of permutation test is described in the thesis as well as approach to search of the most powerful tests to specific alternatives. In the second part of the thesis there are comparisons of powers of parametric, permutation and rank test using simulations. The result is that power of parametric and permutation test are very similar most of the times and that confirms that permutation tests are useful tool for praxis. Keywords: Permutation tests, Exact tests, Hypothesis testing, Power of tests
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Hypotheses Testing in Financial Time Series
Kubů, Jan ; Zichová, Jitka (advisor) ; Jonáš, Petr (referee)
Financial data often take the form of time series. In such cases, their analysis is performed using statistical methods for time series. The thesis describes selected parametric and nonparametric tests of random walk hypothesis. Tests are designed against common mutual correlation alternatives but also against trend and cyclic data structure alternatives. The thesis provides the theoretical basis of these tests and their application to real financial data.
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Comparison of spirometric instruments' precision
Chmelíková, Lucie ; Janoušek, Oto (referee) ; Slávik, Vladimír (advisor)
This thesis deals with pulmonary testing with emphasis to spirometry. In the first part is introduced and described pulmonary system and its attributes. There is a clear and complete list of pulmonary characteristics and parameters. It contains integrated summary of principles that are used for pulmonary measurement devices. First part is followed by description of created virtual device using LabVIEW programming. Simple meter of lung volumes can easily create spirometric curve and automatically evaluate desired values of volume. Program is further enhanced with optional archiving of measured spirometric curve. The last part of this thesis uses statistic testing for deciding of validity or invalidity of hypothesis. By statistic testing of hypothesis we are gaining and expanding basic knowledge about spirometric devices.
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