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A Software Tool for Analyzing Stochastic Data
Lipták, Juraj ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
This thesis discusses the possibility of modeling stochastic processes. Elements of the system with the source of randomness in some cases may be represented by probability distribution. The reader will be acquainted with methods of statistical induction for selecting suitable distribution and generating random numbers. Tool developed in this project aims to propose appropriate probability distribution based on empirical data and provide random variable generating with proposed distribution.
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Hypothesis Testing of interest rates models
Petrík, Daniel ; Myška, Petr (advisor) ; Hurt, Jan (referee)
V předložené práci se zabýváme problematikou stochastického modelování úro- kových sazeb. Jedním z nejobvyklejších postup· je modelovat dynamiku úroko- vých sazeb pomocí stochastické diferenciální rovnice difúze, jejímiž základními kameny jsou funkce driftu a funkce difúze. Od 70. let 20. století byla navržena celá řada model· tohoto typu, a ačkoli se tyto modely neustále zdokonalují, vyvstává přirozená otázka, zda se historicky pozorované úrokové sazby skutečně takovými difúzními rovnicemi řídily. V této práci budeme právě uvedenou hypo- tézu testovat pro několik nejběžnějších jednofaktorových model· úrokové sazby první generace. Z historických dat odhadneme obecnou momentovou metodou a metodou maximální věrohodnosti parametry jednotlivých difúzních rovnic a následně provedeme statistické testy dobré shody proložení těchto rovnic pozo- rovanými daty. 1
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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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Distribution of interpoint distances
Horská, Šárka ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
This thesis investigates basic properties of the interpoint distances be- tween random vectors drawn from multinomial distribution. We also describe a possible application to testing sparse observations, i.e., a setup with small number of observations and large number of categories, where the classical χ2 -test cannot be recommended. As an alternative, utilizing the multinomial interpoint distances, we will present the test statistic proposed by Biswas and Ghosh (2014). 1
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Tests for the Poisson distribution
Trusina, Filip ; Pawlas, Zbyněk (advisor) ; Nagy, Stanislav (referee)
In this work we deal with the question whether a sequence of independent identically distributed random variables comes from the Poisson distribution. For this task we present two different approaches and couple of tests for each appro- ach. The first approach is based on the asymptotic approximation of distribution of test statistics. The second approach uses generation of test samples. Based on simulations done by us, we discuss the power of individual tests and their advantages and disadvantages. 1
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Score tests in contingency tables
Jex, Martin ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
The thesis deals with testing of hypotheses in multinomial distribution. It utilizes two approaches, Pearson's approach known as the of goodness of fit test and the approach stemming from theory of maximum likelihood. The thesis presents derivations of tests based on maximum likelihood. Both approaches are used on the multinomial distribution and for both cases with and without nuisance parameters. The links between both approaches are presented as well. Furthermore both approaches are illustrated on real data to facilitate better understanding of the discussed problems. 1
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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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Hypothesis Testing of interest rates models
Petrík, Daniel ; Myška, Petr (advisor) ; Hurt, Jan (referee)
V předložené práci se zabýváme problematikou stochastického modelování úro- kových sazeb. Jedním z nejobvyklejších postup· je modelovat dynamiku úroko- vých sazeb pomocí stochastické diferenciální rovnice difúze, jejímiž základními kameny jsou funkce driftu a funkce difúze. Od 70. let 20. století byla navržena celá řada model· tohoto typu, a ačkoli se tyto modely neustále zdokonalují, vyvstává přirozená otázka, zda se historicky pozorované úrokové sazby skutečně takovými difúzními rovnicemi řídily. V této práci budeme právě uvedenou hypo- tézu testovat pro několik nejběžnějších jednofaktorových model· úrokové sazby první generace. Z historických dat odhadneme obecnou momentovou metodou a metodou maximální věrohodnosti parametry jednotlivých difúzních rovnic a následně provedeme statistické testy dobré shody proložení těchto rovnic pozo- rovanými daty. 1
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A Software Tool for Analyzing Stochastic Data
Lipták, Juraj ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
This thesis discusses the possibility of modeling stochastic processes. Elements of the system with the source of randomness in some cases may be represented by probability distribution. The reader will be acquainted with methods of statistical induction for selecting suitable distribution and generating random numbers. Tool developed in this project aims to propose appropriate probability distribution based on empirical data and provide random variable generating with proposed distribution.
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Analysis framework for developing cross-platform mobile applications using HTML technology.
Voldřich, Martin ; Pavlíčková, Jarmila (advisor) ; Hrubý, Jan (referee)
The aim of the master thesis is to assess frameworks that are used for development of multiplatform cell phone applications supported by HTML technology. The theoretical part is focused to current market analysis, mobile access issues and the issue of difficulties in specific cases of their application. Analysis is followed by choice of evaluation criteria for setting the most appropriate architecture. Selected evaluation criteria will be used as a tool for detecting of the optimal technology's possibility, which is the most appropriate possibility for development of basic cell phones applications. The practical part is focused to choosing of new evaluation criteria, which helps to create specific questionnaire research. The confirmation or refuse of the hypothesis set up the level of criteria's severity. Based on criteria there will be selected and analysed six of the most used hybrid frameworks. Two of the frameworks with the highest ratings will be tested by real basic cell phone application. The conclusion of the thesis will be follow up by tested frameworks. The frameworks will be described and measured by the author's development experiences.
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