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Epidemiological modeling of Covid-19
Schubert, Richard ; Kašpar, Jakub (referee) ; Mézl, Martin (advisor)
This thesis deals with the continuous epidemiological deterministic compartmental models and the COVID-19 pandemic modeling distinctive features. The effect of different probability distributions of individuals stay in compartments is studied numerically in relation to basic reproductive number and the final size of the epidemic, respectively. New model for a retrospective analysis of the first half of 2020 northern Italy epidemiological data is proposed. The model parameters estimation is performed using minimisation of weighted sum of squared residuals and the search through parameter space with BFGS algorithm implementation.
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GOF tests for gamma distribution
Klička, Petr ; Hlávka, Zdeněk (advisor) ; Kulich, Michal (referee)
The Bachelor thesis deals with the goodness of fit test for the Gamma distribution. Initially, we show several ways how to estimate the parameters of the Gamma distribution - firstly, the maximum likelihood estimator is presented, followed by estimator gained by the method of moments and fi- nally, we introduce the new estimator based on the sample covariance. The last estimator is used for constructing the goodness of fit test for the Gamma distribution. We define the test statistics V ∗ n to this test and its asymptotic normality is derived under the assumption of the null hypothesis. At the end of the thesis the simulations are realized to obtain the empirical size of the test for various values of parameter a and parameter b which equals one. 1
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Epidemiological modeling of Covid-19
Schubert, Richard ; Kašpar, Jakub (referee) ; Mézl, Martin (advisor)
This thesis deals with the continuous epidemiological deterministic compartmental models and the COVID-19 pandemic modeling distinctive features. The effect of different probability distributions of individuals stay in compartments is studied numerically in relation to basic reproductive number and the final size of the epidemic, respectively. New model for a retrospective analysis of the first half of 2020 northern Italy epidemiological data is proposed. The model parameters estimation is performed using minimisation of weighted sum of squared residuals and the search through parameter space with BFGS algorithm implementation.
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GOF tests for gamma distribution
Klička, Petr ; Hlávka, Zdeněk (advisor) ; Kulich, Michal (referee)
The Bachelor thesis deals with the goodness of fit test for the Gamma distribution. Initially, we show several ways how to estimate the parameters of the Gamma distribution - firstly, the maximum likelihood estimator is presented, followed by estimator gained by the method of moments and fi- nally, we introduce the new estimator based on the sample covariance. The last estimator is used for constructing the goodness of fit test for the Gamma distribution. We define the test statistics V ∗ n to this test and its asymptotic normality is derived under the assumption of the null hypothesis. At the end of the thesis the simulations are realized to obtain the empirical size of the test for various values of parameter a and parameter b which equals one. 1
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Retail loan repayment analysis using generalized linear models
Šolc, Michal ; Jarošová, Eva (advisor) ; Forbelská, Marie (referee)
This Diploma thesis concern with generalized linear models and their application in bank practice. Especially to analyze retail loan repayment. First of all we see into theoretical viewpoint of generalized linear models. We shortly try to summarize problems of clasical linear model restrictions and after that we apply to theory on which generalized models are based. We introduce an overview of generalized linear models and after that we concern models, where dependent variable have multinomial and gamma distribution in detail. Main part this thesis is dedicated to data analysis about bank retail loans repayments. In this analysis we use those early mentioned models. We try to create good statistical models on which base the risk ratio of current bank clients could be predicted. The risk ratio is measured by two main indicators, which are: "overdue time" and "overdue amount". For analysis is used statistical software SAS.
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