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Model with Weibull responses
Konečná, Tereza ; Karpíšek, Zdeněk (oponent) ; Hübnerová, Zuzana (vedoucí práce)
This Master's thesis deals with the Weibull model, exactly the two-parametric Weibull distribution. The thesis deals with the estimation of parameters by four way of method of quantiles, by method of maximum likelihood and by graphical method Weibull probability plot. The derivation of parameter estimation methods in the one-way ANOVA type models with Weibull distribution was presented. Relations for the model with constant scale parameter alpha, constant shape parameter beta and the model with both parameters constant were derived. Also the tests with nuisance parameters are included, namely the score test, the Wald test, and the likelihood ratio test. The last chapter deals with the applications of the methods. A comparison of the different methods are demonstrated by graphs, histograms and tables. The methods are programmed in freeware R software. The functionality and properties of each method are verified on two sets of simulated data. In the end of the chapter tree simulated random samples are analysed.
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Application of count data models
Reichmanová, Barbora ; Hampel,, David (oponent) ; Hübnerová, Zuzana (vedoucí práce)
When analysing the data on emergence of plants in a row of a given length, we should consider both the probability of a seed to grow successfully and a random number of seeds sown. That is why this thesis is adressing the random sums, where number of independent identically distributed summands is random number independent of the summands. The first part of the thesis focuses on the theoretical basis, where the term random sum is introduced together with various properties, numerical and functional characteristics outlining the distribution. Afterwards the method of maximum likelihood estimation is discussed, followed by generalized linear models. Moreover, the quasilikelihood method is described briefly. Throughout this part, the theory is illustrated with examples related to the initial problem. The application on real data is discussed in the last chapter.
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Regresní analýza prostorově a časově distribuovaných dat
Rosecký, Martin ; Hübnerová, Zuzana (oponent) ; Bednář, Josef (vedoucí práce)
V práci byly shrnuty poznatky z oblasti prognózování komunálního odpadu (KO). Byly popsány základní informace týkající se lineární regrese a korelační analýzy. Byla provedena analýza vlivů dostupných faktorů na úrovni obcí s rozšířenou působností (ORP). Výsledné modely objasňují až 99 % variability. Modely pro množství odpadu na osobu vysvětlují 12 až 75 % variability. Variabilita KO na osobu vysvětlená modelem je cca o 20 % menší, než u srovnatelné studie, která však používá běžně nedostupná data. Modely jsou pro oblast odpadového hospodářství (OH) použitelné a jejich zdánlivá jednoduchost je v praxi výhodou.
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Selected random variables transformations used in classical linear regression
Tejkal, Martin ; Michálek, Jaroslav (oponent) ; Hübnerová, Zuzana (vedoucí práce)
Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.
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Models with Touchard Distribution
Ibukun, Michael Abimbola ; Karpíšek, Zdeněk (oponent) ; Hübnerová, Zuzana (vedoucí práce)
In 2018, Raul Matsushita, Donald Pianto, Bernardo B. De Andrade, Andre Cançado & Sergio Da Silva published a paper titled ”Touchard distribution”, which presented a model that is a two-parameter extension of the Poisson distribution. This model has its normalizing constant related to the Touchard polynomials, hence the name of this model. This diploma thesis is concerned with the properties of the Touchard distribution for which delta is known. Two asymptotic tests based on two different statistics were carried out for comparison in a Touchard model with two independent samples, supported by simulations in R.
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Matematické modely způsobilosti procesu
Horník, Petr ; Hübnerová, Zuzana (oponent) ; Bednář, Josef (vedoucí práce)
V této diplomové práci se nejprve budeme zabývat ověřením normality a dalších potřebných předpokladů. Dále se seznámíme s transformacemi, abychom mohli i nenormálně rozdělená data převést na normální a provést analýzu způsobilosti. Popíšeme si konstrukci regulačních diagramů, nástroje na posouzení stability procesu. S jejich pomocí můžeme nalézt nežádoucí vymezitelné příčiny a získat tak proces, ve kterém působí pouze náhodné příčiny - statisticky zvládnutý proces. Nakonec zavedeme indexy způsobilosti a výkonnosti pro normální i nenormální data a prozkoumáme některé jejich vlastnosti a úskalí. Diplomovou práci završíme využitím poznatků při výpočtu způsobilosti reálného procesu.
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Modification of Regression Function
Popoola, Seyi James ; Hübnerová, Zuzana (oponent) ; Žák, Libor (vedoucí práce)
The regression analysis is a modelling technique that establishes, mathematically, the relationship between entities of a particular subject. Although the modelling is done in such a way that one variable is seen as a subject of the other(s), regression does not imply causation. The modeling has assumptions such as linearity, normality, little or no multicollinearity, homoscedasticity as conditions for optimal relationship establishment. The simplest of the regression technique is the linear regression which also is the most commonly used. It involves the use of a straight line model to define the best pattern of relationship. This best pattern is assessed by the measure of goodness of fit which describes the amount of variation in the response variable explained by the stimuli (or stimulus). Change-point regression is a type of linear regression that takes into account a change in course of the movement of the relationship under study. This type of change in course is taken into account by modelling the regression in segments to account for the entire relationship observable in the data at hand. Several information criterions are used for detecting this change in course, the Schwartz Information Criterion (SIC), the Bayesian Information Criterion (BIC), amongst others. The detection method adopted for this work is the Modified Information Criterion (MIC) which tests a null hypothesis of no change point against an alternative that states presence of change-point. The data upon which this methodology is applied is the Italy COVID-19 data. The data was subjected to a linear regression and evaluated after which it was subjected to this change point test and the test shows the presence of a change in course. The sections which the test divides the data into were modelled individually and their regression lines were obtained. The two sections were plotted on a graph with their regression lines intercepting at the crest of the plot.
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Time series dynamic factor analysis
Slávik, Ľuboš ; Michálek, Jaroslav (oponent) ; Hübnerová, Zuzana (vedoucí práce)
This thesis studies a novel approach to time series clustering based on a dynamic factor model. Dynamic factor model is a dimension reduction technique enhancing classical factor analysis by a requirement of an autocorrelation structure of the latent factors. Parameters of the model are estimated via EM algorithm employing Kalman filtering and smoothing and necessary restrictions are placed on the model, so the model becomes identifiable. After describing the theoretical concept of the approach, the dynamic factor model is applied to the real observed time series and the work discusses its behaviour and properties on one-month meteorological data of fire weather index at 108 fire stations located in British Columbia. The procedure of the model estimates a loadings matrix of the model with a corresponding small number of latent factors and a variance-covariance matrix of the modeled time series. The thesis applies k-means clustering to the resulted loadings matrix and provides a division of the stations into clusters based on the reduced dimensionality of the original data. With the estimated cluster means and the latent factors, it is possible to obtain particular mean trends for each cluster. Then, the achieved clusters are compared with the results obtained for the same set of stations but within a different month to assess the stability of the clustering. The work discusses the effect of varimax rotation on the loadings matrix as well. Moreover, the thesis suggests a method for detecting possible time series outliers based on the estimated variance-covariance matrix of the model and discusses the effect of outliers on the estimated model.
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Porovnání testů nulovosti korelačního koeficientu dvou normálních náhodných veličin
Kalenský, Vít ; Žák, Libor (oponent) ; Hübnerová, Zuzana (vedoucí práce)
Práce se zabývá srovnáním testů nulovosti korelačního koeficientu dvou normálních náhodných veličin pomocí T statistiky, Fisherovy transformace, Hotellingovy transformace a Haddad-Provostovy statistiky. Obsahuje odvození testů a jejich silofunkcí, které následně porovnává vzájemně mezi sebou a s hodnotami získanými z nasimulovaných náhodných výběrů v programu MATLAB. Na závěr práce jsou vysvětleny a popsány výsledky. Nechybí zde také teoretický úvod k dané problematice.
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Autonomní jednokanálový deinterleaving
Tomešová, Tereza ; Žák, Libor (oponent) ; Hübnerová, Zuzana (vedoucí práce)
Tato práce se zabývá autonomním jednokanálovým deinterleavingem. Autonomní jednokánálový deinterleaving je proces separace přijaté sekvence radiolokačních impulzů od více emiterů na sekvence od jednotlivých emiterů, který jep rováděn bez lidské pomoci. Metody využívané pro úlohu deinterleavingu lze rozdělit dle počtu parametrů používaných pro separaci a to na jednoparametrické a víceparametrické metody. Tato práce se zabývá metodami především víceparametrickými. Jako vhodné metody pro autonomní jednokanálový deinterleaving byly vybrány DBSCAN algoritmus a variační bayesovské metody. Vybrané metody byly upraveny pro úlohu deinterleavingu a implementovány v programovacím jazyce Python. Jejich účinnost byla ověřena na simulovaných datech a datech z reálného provozu.
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