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Probability calculator in MS Excel
Ginzl, Michal ; Malá, Ivana (advisor) ; Vrabec, Michal (referee)
The main aim of this thesis is to perform analytical methods for estimating the most commonly used survival distributions. There are introduced the maximum likelihood estimates of the parameters for the exponential, log-normal, gamma, logistic, Gumbel and Weibull distributions without data censored. For some distributions are mentioned probability plotting and how to estimate parameters with method of least squares or by method of moments. There are discussed tests of goodness of the best fitting distribution. Two tests are based on log-likelihood function and another on test of hypothesis. Practical part of this paper forms application programmed in VBA in MS Excel. Main part of this application includes: module for probability calculations, graphs editor and module for data analysis.
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Transformations of random variables
Šára, Michal ; Marek, Luboš (advisor) ; Malá, Ivana (referee)
This bachelor thesis deals with the transformation of random variables,which plays a significant partv in the theory of probability. The main aim of this paper is to show few methods and techniques which are used when transforming random variables. At the very beginning of this paper one can find a definition and practical examples of the Lebesgue-Stieltjes integral and probability measure, which are nowdays present in every book dealing with modern explanation of theory of probability.
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The use of the lognormal distribution in analysing of earning
Nedvěd, Jakub ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
Object of this thesis is to verify the possibility of use the lognormal distribution as a revenue-distribution model. This text describes characteristics of lognormal distribution and methods of estimating its parameters. Thesis is focused on three-parametric lognormal distribution, because it is most common in this dilemma. Using data from Informational system of average earnings this thesis finds out quality of models. There are described options of usage the lognormal distribution in analyzing revenues. At the end of this essay is suggested an easy analysis of differences between revenue-frequency distribution in the years 2000 and 2010. The thesis demonstrates the fact that the curve of lognormal distribution density function is applicable model which is reliable especially in the wide central part of revenue-distribution.
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Geometric probability
Březinová, Eliška ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
This thesis deals with geometric probability applied on practical exercises. It covers Buffon's needle problem in detail; Laplace's conclusions about pi are supported by my own trial. Next, Bertrand's paradox is solved, and the conclusions are demonstrated on computer programs, which simulate the experiment. One chapter is dedicated to eight different exercises, which can be often found in textbooks. In the end we will mention practical usage of geometric probability, especially in the medicine field. We will point out to usage of modified Buffon's principle, which is used to estimate lengths of planar structures.
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Analysis of the development of hotel business in the Czech Republic and neighboring countries and the impact of financial crisis in this area
Sakharova, Evgenia ; Bílková, Diana (advisor) ; Malá, Ivana (referee)
Hotel businesses in Czech republic has changed dramatically in last 20 years. Therefore, it is interesting to follow its development and see the most influential aspects in this area. However, so far there are none publicly available studies of Czech hotel industry development. The aim of this thesis is to explore the various phases the industry went through and point out those factors which influenced the current situation the most. First of all, the analysis of the development in Czech republic is presented. Consequently, the comparison to the neighbor states is discussed to show relatively how well or bad the business was evolving. The thesis is based on statistical models created with the software STATGRAPHICS and Excel. The gained results show that one of the main reasons of the current downfall is the ever higher market supply. On the other hand, the always blamed economical crises, proved to have lesser influence upon the downfall than originally expected. Finally, the thesis states the reasons of the decreasing occupancy and proposes an increase in the quality of service as a possible solution.
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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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