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Statistical analysis of samples from the generalized exponential distribution
Votavová, Helena ; Popela, Pavel (referee) ; Michálek, Jaroslav (advisor)
Diplomová práce se zabývá zobecněným exponenciálním rozdělením jako alternativou k Weibullovu a log-normálnímu rozdělení. Jsou popsány základní charakteristiky tohoto rozdělení a metody odhadu parametrů. Samostatná kapitola je věnována testům dobré shody. Druhá část práce se zabývá cenzorovanými výběry. Jsou uvedeny ukázkové příklady pro exponenciální rozdělení. Dále je studován případ cenzorování typu I zleva, který dosud nebyl publikován. Pro tento speciální případ jsou provedeny simulace s podrobným popisem vlastností a chování. Dále je pro toto rozdělení odvozen EM algoritmus a jeho efektivita je porovnána s metodou maximální věrohodnosti. Vypracovaná teorie je aplikována pro analýzu environmentálních dat.
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Stochastic Modeling of Data Sets
Orgoník, Svetoslav ; Michálek, Jaroslav (referee) ; Karpíšek, Zdeněk (advisor)
Master's thesis is focused on implementing modern statistical methods for fitting propability distribution using kernel estimates with regard to the possibilities of their implementation on the PC and the application of specic data sets. Master's thesis is a part of project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.
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Dependence Measures
Janda, Radek ; Fusek, Michal (referee) ; Michálek, Jaroslav (advisor)
This thesis focuses on characteristics of the dependence measures among random quantities, as well as its use in industry. The theoretical part focuses on examples of the characteristics used. Furthermore, the software Statistica is described here, for its possibilities of implementing such characteristics. On simple examples, the use of dependence measures is shown. In the practical part, the thesis focuses on statistical analysis of real industrial data, whilst implementing the theory mentioned above.
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Sampling procedures for inspection by attributes
Bartušek, Petr ; Fusek, Michal (referee) ; Michálek, Jaroslav (advisor)
This bachelor´s thesis deals with a description of sampling procedures for inspection by attributes. In the thesis there are described three discrete probability distributions – hypergeometric distribution, binomial distribution and Poisson distribution, including the convergence of their probability mass functions and cumulative distribution functions. The main aim of the thesis is a determination of a sampling plan for sampling procedures for inspection by attributes. The thesis is supplemented with three created programs, which are programmed in software Matlab.
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Statistical analysis of ROC curves
Kutálek, David ; Bednář, Josef (referee) ; Michálek, Jaroslav (advisor)
The ROC (Receiver Operating Characteristic) curve is a projection of two different cumulative distribution functions F0 and F1. On axis are values 1-F0(c) and 1-F1(c). The c-parameter is a real number. This curve is useful to check quality of discriminant rule which classify an object to one of two classes. The criterion is a size of an area under the curve. To solve real problems we use point and interval estimation of ROC curves and statistical hypothesis tests about ROC curves.
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Statistics of extremes
Fusek, Michal ; Neubauer, Jiří (referee) ; Michálek, Jaroslav (advisor)
The thesis deals with extreme value distributions. The theoretical part is devoted to the basics of extreme value theory and to the characterization of extreme value distributions. There is the limit theorem for distributions of the maximum formulated and characteristics of the extreme value distributions deduced. There are parameter estimates for Weibull, lognormal and exponential distributions inferred using method of maximum likelihood and method of moments. There is also the theory of censored samples described. The practical part is devoted to statistical analysis of rainfall.
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The choice of the best somatotype for a given sport using factor analysis
Bušík, Peter ; Fusek, Michal (referee) ; Michálek, Jaroslav (advisor)
This bachelor’s thesis deals with factor model, which is used for data reduction. The purpose is to find unobservable common factors, by which we are able to simply describe observed data. The thesis presents an estimation for parameters of factor analysis by the principal component method, a factor rotation by the varimax method and a way of estimating factor scores by the regression method. Using the computing programme STATISTICA, we apply the factor analysis on the data set, obtained in Korfball. Based on the results, we try to determine the best somatotype for players of this sport.
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Non-parametric estimation of parameters of extreme value distribution
Blachut, Vít ; Popela, Pavel (referee) ; Michálek, Jaroslav (advisor)
The concern of this diploma thesis is extreme value distributions. The first part formulates and proves the limit theorem for distribution of maximum. Further there are described basic properties of class of extreme value distributions. The key role of this thesis is on non-parametric estimations of extreme value index. Primarily, Hill and moment estimator are derived, for which is, based on the results of mathematical analysis, suggested an alternative choice of optimal sample fraction using a bootstrap based method. The estimators of extreme value index are compared based on simulations from proper chosen distributions, being close to distribution of given rain-fall data series. This time series is recommended a suitable estimator and suggested choice of optimal sample fraction, which belongs to the most difficult task in the area of extreme value theory.
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Statistical Classification Methods
Barvenčík, Oldřich ; Žák, Libor (referee) ; Michálek, Jaroslav (advisor)
The thesis deals with selected classification methods. The thesis describes the basis of cluster analysis, discriminant analysis and theory of classification trees. The usage is demonstrated by classification of simulated data, the calculation is made in the program STATISTICA. In practical part of the thesis there is the comparison of the methods for classification of real data files of various extent. Classification methods are used for solving of the real task – prediction of air pollution based of the weather forecast.
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Statistical Modelling of Air Pollution by Dust Aerosol
Čampulová, Martina ; Karpíšek, Zdeněk (referee) ; Michálek, Jaroslav (advisor)
The diploma thesis deals with multivariate statistical methods and their environmental applications. The theoretical part is devoted to selected methods of linear regression analysis, method of principal components and the model of classical and robust factor analysis is also described. In the practical part of thesis, the main emission sources of PM1 aerosols in summer and winter period in Brno and Šlapanice are determined by using the classical factor analysis. The main aerosol emission sources in summer and winter in Šlapanice are also identified by using the robust factor analysis. Furthermore, the prediction of concentrations of PM1 aerosols in summer and winter period in Brno and Šlapanice is performed by using the linear regression model.
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