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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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Cure-rate models
Drabinová, Adéla ; Kulich, Michal (advisor) ; Omelka, Marek (referee)
In this work we deal with survival models, when we consider that with positive probability some patients never relapse because they are cured. We focus on two-component mixture model and model with biological motivation. For each model, we derive estimate of probability of cure and estimate of survival function of time to relaps of uncured patients by maximum likelihood method. Further we consider, that both probability of cure and survival time can depend on regressors. Models are then compared through simulation study. 1
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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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Detection of Differential Item Functioning with Non-Linear Regression: Non-IRT Approach Accounting for Guessing
Drabinová, Adéla ; Martinková, Patrícia
In this article, we present a new method for estimation of Item Response Function and for detection of uniform and non-uniform Differential Item Functioning (DIF) in dichotomous items based on Non-Linear Regression (NLR). Proposed method extends Logistic Regression (LR) procedure by including pseudoguessing parameter. NLR technique is compared to LR procedure and Lord’s and Raju’s statistics for three-parameter Item Response Theory (IRT) models in simulation study based on Graduate Management Admission Test. NLR shows superiority in power at low rejection rate over IRT methods and outperforms LR procedure in power for case of uniform DIF detection. Our research suggests that the newly proposed non-IRT procedure is an attractive and user friendly approach to DIF detection.
Fulltext: content.csg -  PDF
Plný tet: v1229-16-version2 - PDF; v1229-16 - PDF
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