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Survival analysis - probability distributions and their characteristics
Plocová, Michaela ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This bachelor thesis is concerned with probability distributions that are used in survival analysis and characteristics of these distributions (survival function, hazard rate, probability density function, mean residual life). The aim of this thesis is to provide a summary of probability distributions and their characteristics, then to graphically represent them and show the shapes they can take in dependence on different parameters of distributions. The thesis is divided in 4 parts, the first three parts are mainly theoretical and they focus on general definitions of the characteristics, the most widely used distributions in survival analysis and mixture distributions. The last part is practical and focuses mainly on graphic representation of the characteristics for separate distributions and different values of parameters. Also, for each distribution measures of location and variability are calculated. The characteristics of mixture distributions are also graphically represented.
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The Six Sigma methodology
Zajícová, Hana ; Jarošová, Eva (advisor) ; Malá, Ivana (referee)
Bachelor thesis deals with the desription of the statistical foundations and individual steps of Six Sigma, which are descibed by the DMAIC model. The thesis focuses on statistical process control and control charts. The main goal is to evaluate the possible use of control charts for attributes, namely the control chart for fraction nonconforming or p-diagram and to describe its properties expressed by the operating characteristic (OC). The influence of the sample size on the OC curve is examined. The last part of this theses deals with the desription of the xi-diagram as an alternative of the p-diagram. The properties of this alternative and classical p-diagram are compared.
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Application of generalized linear model for mixture distributions
Pokorný, Pavel ; Malá, Ivana (advisor) ; Pavelka, Roman (referee)
This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.
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Estimates in Survival Analysis
Čabla, Adam ; Malá, Ivana (advisor) ; Tomášek, Ladislav (referee)
This thesis introduces methods used in time-to-date analysis. It is written generally and so usable in dealing with any example. The thesis deals with problem of censoring, which means, that some observations occurred after the following, which is typical for the lifetime analysis. Methods mentioned in the thesis are nonparametric and parametric estimates of the survival function and their characteristics, and regression models, concretely Cox model and accelerated failure time model, which examine effect of the covariates on survival function. In the thesis is beside survival function presented hazard function, which express intensity of the analyzed event and cumulative hazard function, which is created as the name suggests by cumulative summation of the hazard function. Estimates of these functions are obtainable from survival function and for parametric estimate often exists formula resulting from parameters of used distribution. Empirical part of the thesis introduces influence of several different types and degrees of censoring on parametric and nonparametric estimates of the survival function, mean and median. The other empirical example is the usage of regression analysis on the data from the lungs cancer research made by Mayo Clinic.
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Nonparametric estimations in survival analysis
Svoboda, Martin ; Malá, Ivana (advisor) ; Tomášek, Ladislav (referee)
This work introduces nonparametric models which are used in time to event data analysis. It is focused on applying these methods in medicine where it is called survival analysis. The basic techniques and problems, which can appear in survival analysis, are presented and explained here. The Kaplan -- Meier estimator of survival function is discussed in the main part. This is the most frequented method used for estimating the survival function in patients who have undergone a specific treatment. The Kaplan -- Meier estimator is also a common device in the statistical packets. In addition to estimation of survival function, the estimation of hazard function and cumulative hazard function is presented. The hazard function shows the intensity of an individual experiencing the particular event in a short time period. Special problems occur when analyzing time to event data. A distinctive feature, often present in such data, is known as censoring. That is the situation when the individual does not experience the event of interest at the time of study. The thesis covers also an empiric part, where the results of an analysis of patients with the larynx carcinoma diagnosis are shown. These patients were treated in a hospital located in České Budějovice. This analysis is based on a theory presented in the previous chapters.
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Statistical analysis of students' success rate in 4ST201
Vanišová, Adéla ; Malá, Ivana (advisor) ; Bašta, Milan (referee)
The main goal of this thesis is the statistical comparison of results from students who attended the course 4ST201. The data used are for the winter semester of the academic year 2008/2009. This thesis is focused on the results throughout semester and the final exam. The thesis is divided into two main chapters. The first part is a theoretical base for the calculation and it also contains information about data I worked with. The second part is a practical part and it is focused on interpretation of the results of the analysis where I examined the students' results from different aspects and tested hypotheses about interdependencies. In the conclusion findings from all calculations are summarized.
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Analysis of students' results of the subject 4ST201
Šulc, Zdeněk ; Malá, Ivana (advisor) ; Helman, Karel (referee)
The main aim of this bachelor thesis is to compare and to test the results of students, who attended the course of statistics at the University of Economics in Prague. The thesis is divided into theoretical and practical part. The theoretical part explains basic methods which are used in the thesis. The practical part deals with an analysis which is mainly focused on mid-term tests. The results of this thesis are summarized in the conclusion.
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Verification of normality
Zimmerhaklová, Tereza ; Jarošová, Eva (advisor) ; Malá, Ivana (referee)
The goal of my Bachelor thesis on "Verification of normality" is to provide an overview of various methods of verification of normality. That is test graphical methods, testing normality occurring in the statistical programs and selected statistical tests to test the effectiveness of the randomly generated data. The importance of testing normality, numerically and graphically, both based on the fact that many statistical analyses assume a normal distribution: analysis of variance, t-tests or multiple regression. Testing of normality allows make conclusions on the basis of the investigation of choice for the whole population in relation to confidence intervals and hypotheses tests.
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Random walk and game theory
Vondrušková, Ivana ; Malá, Ivana (advisor) ; Novák, Ilja (referee)
A random walk is a mathematical formalization of a trajectory that consists of taking succesive random steps. The results od random walk analysis have been applied to computer science, economics, biology tec. This thesis is concentrated on connection between random walk and games theory especially with thinglering simulation. The application part of this thesis is focused on game strategies, that determine the amount of bet in next game.
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Students results in statistics
Knapová, Petra ; Malá, Ivana (advisor) ; Novák, Ilja (referee)
The main aim of my thesis is to compare results of different groups of students who took part in the statistic course on VŠE. The thesis is dividend into two parts. The first part is focused on theoretical solution of used data comparison. The second part is practical and it is focused on results comparison from different angles with descriptive statistics and some statisistics tests. The results from partial comparison of data from different points of view are summarized at the end of the thesis.
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