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Paradoxes in Probability Theory and Mathematical Statistics
Klouparová, Zdeňka ; Omelka, Marek (advisor) ; Stibůrek, David (referee)
In this work I deal with few selected paradoxes related to games. First of all I explain a paradox directly from the game theory field. I show that kids' game about matching fingers is advantageous for one player although it seems to be fair for both players at the first sight. Second example touches war troubles with hidden objects. In the second chapter I explain the Gladiator paradox and I try to find the best order in which the gladiators should be sent to an arena to fight. Finally, I also touch the paradox of transitivity and explain how the game with nontransitive dices works. Keywords: Game theory paradox, Gladiator paradox, paradox of transitivity 1
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Analysis of equilibria in economic models
Stibůrek, David ; Pražák, Dalibor (advisor) ; Hencl, Stanislav (referee)
Nazev pracc: Analyza roviiovaznych bodu v ekonomickycli rnodelech Autor: David Stiburek Katcdra (ustav): Katedra matcmatickc analyzy Vcdouci bakalarske prace: UNDr. Dalibor Prazak, Ph.D. (- -mail vedouciho: ra'/akiojkarli Abstrakt: V pfcdlozcne praci studujcme rovnovahu v ekonomickycli mode- Icch. V fade ekonomickycli situacicli muzcrnc pozorovat, zc nastanc rovno- vazna situce neboli, ze od urciteho okamziku nenastauou zadne velke zmcny. V rnnoha disciplinach bychom si pfali znat tyto rovnovaznc hodnoty. Ovscm inohou byt i situce, kdy v uekterych oblaytech uemusi k rovnovaze vubec dojit. Proto v teto praci nejdfivc zkouinamc, kdy se situace vubec muze do- stat do neja,ke rovuovahy neboli, kdy jc stabilni. A pole sc pokousimo \ircit rovnovaznou hoduotu a take relaxacni cas. Klicova slova: Ilovnovalia, stabilita a relaxacni doba. Title: Aiialysia of equilibria in economic models Author: David Stiburek Department: Department of Mathemathical analysis Supervisor: RNDr. Dalibor Prazak, Ph.D. Supervisor's (vrnail address: pra/ak'iikarliii.nifF.cuiii.rz Abstract: In the present work we study equilibria in ecomomics models. In many states we can see something, what can be simple called ay steady state. In many branches we would like to know these equilibria. But there exist some situations, when we; can't expect...
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Tests of normality of time series
Stibůrek, David ; Anděl, Jiří (advisor) ; Kulich, Michal (referee)
This work considers testing normality of time series in AR and ARMA processes. Firstly we investigate properties of common normality tests, which assume independency. The main goal is to examine levels and powers of tests in dependence on distances of the roots of the characteristic polynom from unit circle. After this we study the tests, which don't assume independency. In the case of AR processes, we get good results by testing normality of residuals. More complex tests can also give good results, but these tests need many observations and are difficult from the numerical point of view.
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Paradoxes in Probability Theory and Mathematical Statistics
Klouparová, Zdeňka ; Omelka, Marek (advisor) ; Stibůrek, David (referee)
In this work I deal with few selected paradoxes related to games. First of all I explain a paradox directly from the game theory field. I show that kids' game about matching fingers is advantageous for one player although it seems to be fair for both players at the first sight. Second example touches war troubles with hidden objects. In the second chapter I explain the Gladiator paradox and I try to find the best order in which the gladiators should be sent to an arena to fight. Finally, I also touch the paradox of transitivity and explain how the game with nontransitive dices works. Keywords: Game theory paradox, Gladiator paradox, paradox of transitivity 1
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Analysis of equilibria in economic models
Stibůrek, David ; Hencl, Stanislav (referee) ; Pražák, Dalibor (advisor)
Nazev pracc: Analyza roviiovaznych bodu v ekonomickycli rnodelech Autor: David Stiburek Katcdra (ustav): Katedra matcmatickc analyzy Vcdouci bakalarske prace: UNDr. Dalibor Prazak, Ph.D. (- -mail vedouciho: ra'/akiojkarli Abstrakt: V pfcdlozcne praci studujcme rovnovahu v ekonomickycli mode- Icch. V fade ekonomickycli situacicli muzcrnc pozorovat, zc nastanc rovno- vazna situce neboli, ze od urciteho okamziku nenastauou zadne velke zmcny. V rnnoha disciplinach bychom si pfali znat tyto rovnovaznc hodnoty. Ovscm inohou byt i situce, kdy v uekterych oblaytech uemusi k rovnovaze vubec dojit. Proto v teto praci nejdfivc zkouinamc, kdy se situace vubec muze do- stat do neja,ke rovuovahy neboli, kdy jc stabilni. A pole sc pokousimo \ircit rovnovaznou hoduotu a take relaxacni cas. Klicova slova: Ilovnovalia, stabilita a relaxacni doba. Title: Aiialysia of equilibria in economic models Author: David Stiburek Department: Department of Mathemathical analysis Supervisor: RNDr. Dalibor Prazak, Ph.D. Supervisor's (vrnail address: pra/ak'iikarliii.nifF.cuiii.rz Abstract: In the present work we study equilibria in ecomomics models. In many states we can see something, what can be simple called ay steady state. In many branches we would like to know these equilibria. But there exist some situations, when we; can't expect...
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Tests of normality of time series
Stibůrek, David ; Kulich, Michal (referee) ; Anděl, Jiří (advisor)
This work considers testing normality of time series in AR and ARMA processes. Firstly we investigate properties of common normality tests, which assume independency. The main goal is to examine levels and powers of tests in dependence on distances of the roots of the characteristic polynom from unit circle. After this we study the tests, which don't assume independency. In the case of AR processes, we get good results by testing normality of residuals. More complex tests can also give good results, but these tests need many observations and are difficult from the numerical point of view.
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