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Normality tests
Kotlorz, Lukáš ; Anděl, Jiří (advisor) ; Sabolová, Radka (referee)
The aim of this thesis focused on testing normality is to describe both statistical tests and graphical methods. The first part is devoted to graphical methods used to testing normality (particularly Histogram, Boxplot and Q-Q Plot). The tests used for testing the conformity of random sample distribution with normal distribution, e.g., Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors, Anderson-Darling, Chi-squared, are described in the second part. The test statistics, the critical region and alternatively the link for tabulated critical values are listed for each test. The simulations, whether the random sample comes from normal distribution, are described in the third part. The samples from di erent distributions were generated by Program R.
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Semi - infinite programming: theory and portfolio efficiency application
Klouda, Lukáš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
Title: Semi-infinite programming: theory and portfolio efficiency application Author: Bc. Lukáš Klouda Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Miloš Kopa, PhD. Supervisor's e-mail address: kopa@karlin.mff.cuni.cz Abstract: The thesis deals with application of semi-infinite programming to a portfolio efficiency testing. The summary of semi-infinite programming, first and second order optimality conditions and duality in linear semi-infinite programming is presented. The optimization problem for a portfolio efficiency testing with respect to the second order stochastic dominance under assumption of discrete, normal, Students and general elliptical distribution is formulated. Conditional value at risk(CVaR) is used as the risk measure, because of its consistency with the second order stochastic dominance relation. Efficiency of index PX with respect to the second order stochastic dominance is tested. The tests are performed using the program GAMS.
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Statistical tests power analysis
Kubrycht, Pavel ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This Thesis deals with the power of a statistical test and the associated problem of determining the appropriate sample size. It should be large enough to meet the requirements of the probabilities of errors of both the first and second kind. The aim of this Thesis is to demonstrate theoretical methods that result in derivation of formulas for minimum sample size determination. For this Thesis, three important probability distributions have been chosen: Normal, Bernoulli, and Exponential.
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Recognition of Poses and Gestures
Jiřík, Leoš ; Hradiš, Michal (referee) ; Zemčík, Pavel (advisor)
This thesis inquires the existing methods on the field of image recognition with regards to gesture recognition. Some methods have been chosen for deeper study and these are to be discussed later on. The second part goes in for the concenpt of an algorithm that would be able of robust gesture recognition based on data acquired within the AMI and M4 projects. A new ways to achieve precise information on participants position are suggested along with dynamic data processing approaches toward recognition. As an alternative, recognition using Gaussian Mixture Models and periodicity analysis are brought in. The gesture class in focus are speech supporting gestures. The last part demonstrates the results and discusses future work.
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Mathematical modelling of crown rate
UHLÍŘOVÁ, Žaneta
This thesis is focused on mathematical modelling of exchange rate CZK/USD in 1991 - 2014. Time series was divided into 5 parts. First Box-Jenkins methodology models were examined, especially ARIMA model. Unfortunately, the model could not be used because none of the time series showed correlation. The time series is considered as a white noise. The data appear to be completely random and unpredictable. The time series have not constant variance neither normal distribution and therefore GARCH volatility model was used as the second model. It is better not to divide time series when using model of volatility. Volatility model contributes to more accurate prediction than the standard deviation. Results were calculated in RStudio software and MS Excel.
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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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Modelling of bed in process of particle saltation in channel
Kharlamova, Irina ; Kharlamov, Alexander A. ; Chára, Zdeněk ; Vlasák, Pavel
For numerical modelling particle saltation in channel with rough bed is important to define a bed configuration. The paper deals with the bed consisting of spherical particles of the different size then the saltating particle. In horizontal x-z plane the particles are arranged hexagonally. In vertical direction the particles are distributed according to Gaussian distribution. Before each collision of the saltating particle with bed the bed is shifted on a random distance and it is rotated by a random angle, so there is uniform probability to find a bed particle in any point of the x-z plane. The bed structure is chosen with aim to represent the natural bed as much as possible, thus the known information about distribution of the bed particles along y-direction is used and the location of bed particles in the x-z plane is controlled by principles of equal probability and minimal dense packing.
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Modeling a distribution of mortgage credit losses
Gapko, Petr ; Šmíd, Martin
One of the biggest risks arising from financial operations is the risk of counterparty default, commonly known as a “credit risk”. Leaving unmanaged, the credit risk would, with a high probability, result in a crash of a bank. In our paper, we will focus on the credit risk quantification methodology. We will demonstrate that the current regulatory standards for credit risk management are at least not perfect, despite the fact that the regulatory framework for credit risk measurement is more developed than systems for measuring other risks, e.g. market risks or operational risk. Generalizing the well known KMV model, standing behind Basel II, we build a model of a loan portfolio involving a dynamics of the common factor, influencing the borrowers’ assets, which we allow to be non-normal. We show how the parameters of our model may be estimated by means of past mortgage deliquency rates.
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Porevoluční vývoj mezd ve zdravotnictví v České republice
Nováková, Kristýna Bc. ; Bartošová, Jitka (advisor) ; Kletečková, Marie (referee)
Analýza porevolučního vývoje mezd ve zdravotnictví v České republice a v Jihočeském kraji se zaměřením na rozdíly v podnikatelské a nepodnikatelské sféře. Dále je nastíněna problematika rovnosti odměňování mužů a žen v České republice. Data pro analýzu jsou použita ze mzdových a platových statistických šetření od ČSÚ, z ÚZIS a Informačního sysému o průměrném výdělku. Data jsou zpracována na základě modelování logaritmicko-normálních rozdělení platů a mezd některých kategorií zaměstnanců ve zdravotnictví.
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