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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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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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Extreme Value Distributions with Applications
Fusek, Michal ; Skalská,, Hana (referee) ; Karpíšek, Zdeněk (referee) ; Michálek, Jaroslav (advisor)
The thesis is focused on extreme value distributions and their applications. Firstly, basics of the extreme value theory for one-dimensional observations are summarized. Using the limit theorem for distribution of maximum, three extreme value distributions (Gumbel, Fréchet, Weibull) are introduced and their domains of attraction are described. Two models for parametric functions estimation based on the generalized extreme value distribution (block maxima model) and the generalized Pareto distribution (threshold model) are introduced. Parameters estimates of these distributions are derived using the method of maximum likelihood and the probability weighted moment method. Described methods are used for analysis of the rainfall data in the Brno Region. Further attention is paid to Gumbel class of distributions, which is frequently used in practice. Methods for statistical inference of multiply left-censored samples from exponential and Weibull distribution considering the type I censoring are developed and subsequently used in the analysis of synthetic musk compounds concentrations. The last part of the thesis deals with the extreme value theory for two-dimensional observations. Demonstrational software for the extreme value distributions was developed as a part of this thesis.
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Extreme Value Distributions with Applications
Fusek, Michal ; Skalská,, Hana (referee) ; Karpíšek, Zdeněk (referee) ; Michálek, Jaroslav (advisor)
The thesis is focused on extreme value distributions and their applications. Firstly, basics of the extreme value theory for one-dimensional observations are summarized. Using the limit theorem for distribution of maximum, three extreme value distributions (Gumbel, Fréchet, Weibull) are introduced and their domains of attraction are described. Two models for parametric functions estimation based on the generalized extreme value distribution (block maxima model) and the generalized Pareto distribution (threshold model) are introduced. Parameters estimates of these distributions are derived using the method of maximum likelihood and the probability weighted moment method. Described methods are used for analysis of the rainfall data in the Brno Region. Further attention is paid to Gumbel class of distributions, which is frequently used in practice. Methods for statistical inference of multiply left-censored samples from exponential and Weibull distribution considering the type I censoring are developed and subsequently used in the analysis of synthetic musk compounds concentrations. The last part of the thesis deals with the extreme value theory for two-dimensional observations. Demonstrational software for the extreme value distributions was developed as a part of this thesis.
|
|
|
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.
|
|
|
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.
|
|
|
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.
|
|
|
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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