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Statistical models for prediction of project duration
Oberta, Dušan ; Žák, Libor (referee) ; Hübnerová, Zuzana (advisor)
Cieľom tejto bakalárskej práce je odvodiť štatistické modely vhodné pre analýzu dát a aplikovať ich na analýzu reálnych dát týkajúcich sa časovej náročnosti projektov v závislosti na charakteristikách projektov. V úvodnej kapitole sú študované lineárne regresné modely založené na metóde najmenších štvorcov, vrátane ich vlastností a predikčných intervalov. Nasleduje kapitola zaoberajúca sa problematikou zobecnených lineárnych modelov založených na metóde maximálnej vierohodnosti, ich vlastností a zostavením asymptotických konfidenčných intervalov pre stredné hodnoty. Ďalšia kapitola sa zaoberá problematikou regresných stromov, kde sú znova ukázané metóda najmenších štvrocov a metóda maximálnej vierohodnosti. Boli ukázané základné princípy orezávania regresných stromov a odvodenie konfidenčných intervalov pre stredné hodnoty. Metóda maximálnej vierohodnosti pre regresné stromy a odvodenie konfidenčných intervalov boli z podstatnej časti vlastným odvodením autora. Posledným študovaným modelom sú náhodné lesy, vrátane ich základných vlastností a konfidenčných intervalov pre stredné hodnoty. V týchto kapitolách boli taktiež ukázané metódy posúdenia kvality modelu, výberu optimálneho podmodelu, poprípade určenia optimálnych hodnôt rôznych parametrov. Na záver sú dané modely a algoritmy implementované v jazyku Python a aplikované na reálne dáta.
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One factor models of interest rates
Jambor, Matúš ; Myška, Petr (advisor) ; Hurt, Jan (referee)
Title: One factor interest rate models Author: Matúš Jambor Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Petr Myška Abstract: In this thesis we looked closely at the models of interest rates that are applied in the area of financial mathematics and actuarial sciences. There are several models that try to describe the behavior of yield curve plausibly. In most of the cases the models stem from probability theory and coincidence. These models are also means for assessment of financial derivates whose price de- pends on the interest rates movements. The work deals with three one-factor models which are analyzed into more details in the second chapter. The last chapter is about real-data calibration. Keywords: one factor models, interest rates, maximum likelihood method 1
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Parameter estimating in time series models
Kostárová, Aneta ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
This bachelor thesis deals with some methods of parameter estimating in linear time series models. The most used approach in software products is the maximum likelihood estimation. The theoretical part explains the parameter estimation of the ARMA model by conditional and unconditional maximum likelihood estimation and demonstrates both methods for lower order models. The practical part examines and describes the imple- mentation of parameter estimating in Mathematica and R software. The comparison of the quality of the estimates calculated by various procedures of the chosen software is included. Finally, the acquired findings is used in a simulation study. 1
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Models of binary time series
Kunayová, Monika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This bachelor thesis deals with the time series of binary variables that exist in many social spheres. The indicator may denote a certain value being exceeded or a phenomenon occurring. We study a model of logistic autoregression and its properties, partial likelihood function which allows us to work with dependent data, and derive useful relationships for a practical application that consists of time series simulation and real data analysis using free software R.
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Zero inflated Poisson model
Veselý, Martin ; Komárek, Arnošt (advisor) ; Hlávka, Zdeněk (referee)
This paper deals with the zero-inflated Poisson distribution. First the Poisson model is defined and generalized to a zero-inflated model. The basic properties of this generalized model are derived. After- wards the basics of the method of moments and the maximum likelihood method are described. Both of these are used to derive parameter estimates of such distribution. The feasibility of calculating the distribution of moment method estimates is analyzed. Then the asymptotic distribution of maximum likelihood estimates is derived and used to create confidence intervals. In the last chapter a numeric si- mulation of the derived asymptotic properties is performed. Special attention is paid to situations where regularity conditions are not met. 1
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One factor models of interest rates
Jambor, Matúš ; Myška, Petr (advisor) ; Hurt, Jan (referee)
Title: One factor interest rate models Author: Matúš Jambor Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Petr Myška Abstract: In this thesis we looked closely at the models of interest rates that are applied in the area of financial mathematics and actuarial sciences. There are several models that try to describe the behavior of yield curve plausibly. In most of the cases the models stem from probability theory and coincidence. These models are also means for assessment of financial derivates whose price de- pends on the interest rates movements. The work deals with three one-factor models which are analyzed into more details in the second chapter. The last chapter is about real-data calibration. Keywords: one factor models, interest rates, maximum likelihood method 1
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Statistical problems in Markov chains with applications in finance
Chudý, Marek ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
Title: Statistical problems in Markov chains with applications in finance Author: Marek Chudý Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: In this work, we study estimation methods for estimating transition probabilities in Markov chains. We discuss two methods, the first one for com- plete data and the second one for aggregate data. In the second chapter, we will introduce the theory for both methods and show examples of tests of sev- eral hypothesis about transition probabilities. In the last chapter we apply both methods to real data comming from an insurance company. In the last chapter we also present the results of both methods and compare them with each other. Keywords: Markov chains, transition probabilities, maximum likelihood method, least squares method
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