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Statistical Analysis of an Organization´s Economic Risk Factors
Ambrožová, Andrea ; Sylva, Šujanová (referee) ; Karpíšek, Zdeněk (advisor)
This thesis deals with the evaluation of high-risk economical factors of one particular organization and consequently with their evaluation based on statistical methods. The principal aim of the study was to determine the dominant economic indicators of the organization and assess their development over time based on statistical methods, using statistical tools. The tools utilized in the thesis were Statgraphics Centurion XV and MS Excel.
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Risk Analysis of Important Factors of Company Using Statistical Methods
Genčurová, Lucie ; Popela, Pavel (referee) ; Karpíšek, Zdeněk (advisor)
This diploma thesis is focusing on the analysis of individual financial indicators of company MARLENKA international s.r.o. using the methods of financial analysis and statistical methods. The financial situation of the company is evaluated based on the results of analyzes. Then the prediction of the evolution of the selected indicators is calculated for the next two years using regression analysis and interval regression analysis. The diploma thesis also addresses potential risk for the company and recommendations for the risk reduction. Following the analyzes, a summary of the company’s financial situation is created.
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Reliability of Technical Systems
Ertl, Jakub ; Šácha, Jakub (referee) ; Karpíšek, Zdeněk (advisor)
The diploma project is focused on investigating the reliability of multi-state technical systems. A summary of the basic conception of renewal theory and stochastic processes is given in this paper. The possibility of solving multi-state systems reliability by using Markov models or simulation is shown. The software Reliab. S. M. S. O. 1.0 was created for solving non-homogeneous series, parallel, series-parallel and parallel-series systems. Outputs of this software are described in chapter 10. This work also contains $\beta$-factor method and theory of common-cause failures. The diploma project was supported by project from MSMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production" and by grant from Grant Agency of the Czech Republic (Czech Science Foundation) reg. no. 103/08/1658 "Advanced optimum design of composed concrete structures".
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Analytical Methods in Motorsport
Růžička, Bronislav ; Dočkal, Aleš (referee) ; Čejka, Václav (referee) ; Karpíšek, Zdeněk (referee) ; Mazůrek, Ivan (advisor)
This dissertation is focused on proposal for simplified data analyze approach for sport-car vehicle dynamic evaluation with relationship to possibility for qualified estimation of set-up parameters influence for overall vehicle performance. In common practice can be usual overlapping effect caused by concurrent changes of car setup elements if performed in the same moment with resulting in not correct or hardly definable process determination for evaluation and decision about next steps in car development. For analyze of these multidimensional data is then chosen process with approach by Linear Regression Model (LRM). In dissertation is proposed basic philosophy with concern on specificity of car vehicle dynamics, performed experiment with defined inputs including analyze and interpretation method of obtained outputs. This methodic take into account also possibility for general application of multidimensional data analyses not only in motorsport, but as well for dynamic behavior diagnostics of technical systems where finding of optimal running condition depends on multi-parametric setup whose combination must reflect often changes of outer conditions too.
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Stochastic Modeling of Data Sets
Orgoník, Svetoslav ; Michálek, Jaroslav (referee) ; Karpíšek, Zdeněk (advisor)
Master's thesis is focused on implementing modern statistical methods for fitting propability distribution using kernel estimates with regard to the possibilities of their implementation on the PC and the application of specic data sets. Master's thesis is a part of project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.
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Statistical Analysis of Real Process Scrap
Širjovová, Zuzana ; Karpíšek, Zdeněk (referee) ; Bednář, Josef (advisor)
Quality, as well as stability of processes check is nowadays gaining on its significance. The main driving force of its increasing importance is the rapid expansion of series production. Large-scale manufacturing processes are concerned, in terms of the number of operators, direct and indirect influence on rejects, but also on process stability. There are several quality characteristics, defined by utility properties, that can be easily measurable (linear dimensions, solidity, elongation, humidity, concentration) or directly immeasurable, mostly subjective (fragrance, taste, color, comfort while using, appearance). Statistical Process Control-SPC features the preventive tool of quality control, because based on the early detection of significant divergences of the process from the predetermined level, it is possible to execute interventions in the process with the aim of maintaining the acceptable and stable level and improving the process. This manufacturing process check will be the topic of my thesis. At first, Shewhart's control charts analysis will be done to determine strong process instability. Consequently, analysis will be carried out in test chi-square, used to determine the influence of each factor on the process of stability (operators, type of shift, type of product, type of defect on the product). All the practical part will be processed in statistical software MINITAB15. The thesis will be complemented by the findings from the examination of the features of interval estimates of parameter p for binomial distribution - numeric stability in the various statistical software (specifically Minitab 15, Statistica, Matlab 7.8.0). Master's thesis was supported by project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.
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Approximations in Stochastic Optimization and Their Applications
Mrázková, Eva ; Horová, Ivana (referee) ; Štěpánek, Petr (referee) ; Karpíšek, Zdeněk (advisor)
Mnoho inženýrských úloh vede na optimalizační modely s~omezeními ve tvaru obyčejných (ODR) nebo parciálních (PDR) diferenciálních rovnic, přičemž jsou v praxi často některé parametry neurčité. V práci jsou uvažovány tři inženýrské problémy týkající se optimalizace vibrací a optimálního návrhu rozměrů nosníku. Neurčitost je v nich zahrnuta ve formě náhodného zatížení nebo náhodného Youngova modulu. Je zde ukázáno, že dvoustupňové stochastické programování nabízí slibný přístup k řešení úloh daného typu. Odpovídající matematické modely, zahrnující ODR nebo PDR omezení, neurčité parametry a více kritérií, vedou na (vícekriteriální) stochastické nelineární optimalizační modely. Dále je dokázáno, pro jaký typ úloh je nutné použít stochastické programování (EO reformulace), a kdy naopak stačí řešit jednodušší deterministickou úlohu (EV reformulace), což má v praxi význam z hlediska výpočetní náročnosti. Jsou navržena výpočetní schémata zahrnující diskretizační metody pro náhodné proměnné a ODR nebo PDR omezení. Matematické modely odvozené pomocí těchto aproximací jsou implementovány a řešeny v softwaru GAMS. Kvalita řešení je určena na základě intervalových odhadů "optimality gapu" spočtených pomocí metody Monte Carlo. Parametrická analýza vícekriteriálního modelu vede na výpočet "efficient frontier". Jsou studovány možnosti aproximace modelu zahrnujícího pravděpodobnostní členy související se spolehlivostí pomocí smíšeného celočíselného nelineárního programování a reformulace pomocí penalizační funkce. Dále je vzhledem k budoucím možnostem paralelních výpočtů rozsáhlých inženýrských úloh implementován a testován PHA algoritmus. Výsledky ukazují, že lze tento algoritmus použít, i když nejsou splněny matematické podmínky zaručující konvergenci. Na závěr je pro deterministickou verzi jedné z úloh porovnána metoda konečných diferencí s metodou konečných prvků za použití softwarů GAMS a ANSYS se zcela srovnatelnými výsledky.
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Model with Weibull responses
Konečná, Tereza ; Karpíšek, Zdeněk (referee) ; Hübnerová, Zuzana (advisor)
Tato diplomová práce se zabývá Weibullovými modely, přesněji dvouparametrickým Weibullovým rozdělením. Práce se zabývá odhady parametrů, a to čtyřmi variantami kvantilové metody, metodou maximální věrohodnosti a grafickou metodou Weibullova pravděpodobnostního grafu. Je uvedeno odvození odhadu parametrů pro jednovýběrovou analýzu rozptylu pro Weibullovo rozdělení. Jsou zde odvozeny vztahy pro model s konstantním parametrem alfa, s konstantním parametrem beta a s oběma konstantními parametry. Také jsou uvedeny testové statistiky pro rušivé parametry - skórový test, Waldův test a test založený na věrohodnostním poměru. V poslední kapitole je provedena aplikace jednotlivých představených metod. Srovnání metod je ukázáno pomocí grafů, histogramů a tabulek. Metody jsou naprogramovány v~softwaru R. Jejich funkčnost a vlastnosti jsme ověřili na dvou simulovaných souborech dat. Diplomová práce je zakončena příkladem tří simulovaných náhodných výběrů, na kterých byla provedena analýza pomocí zavedených metod.
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Risk Analysis of Selected Cryptocurrencies in Personal Finance
Strouhal, Tomáš ; Stroukal,, Dominik (referee) ; Karpíšek, Zdeněk (advisor)
This diploma thesis deals with cryptocurrency’s risk regarding other investment opportunities, such as funds. The aim of the work is to present a simple indicator of risk and reward in order to place cryptocurrencies in the context of other investments. First, selected cryptocurrencies are described, then their characteristics are compared with the funds. Synthetic risk and reward indicator is used as a tool to compare risk and reward of cryptocurrencies with the funds. This indicator is modified to match the cryptocurrency’s characteristics and still have a narrative value. After this modification, it is used to calculate the risk and reward of the S&P 500, Allianz Global Artificial Intelligence, Binance Coin, Bitcoin, Cardano, Ethereum, Solana, Tether, USD Coin and XRP. The results show that the original range of the indicator is insufficient given the higher volatility of cryptocurrencies, which it is unable to reflect. Conversely, the adjusted indicator is already very good at calculating with higher volatility in cryptocurrencies and assigning them to a higher risk class.
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Development and history of probability theory
Michalová, Jitka ; Karpíšek, Zdeněk (referee) ; Žák, Libor (advisor)
This bachelor thesis deals with the history and development of probability and its theory before the introduction of Kolmogorov's axiomatic definition in the 20th century. It follows the Problem of points and its solvers: Luca Pacioli, Niccola Fontana Tartaglia, Blaise Pascal and Pierre de Fermat. It focuses on the works De Ratiociniis in Ludo Aleae by Christiaan Huygens and Ars Conjectandi by Jacob Bernoulli. It also deals with various definitions of probability: classical (Laplac), statistical, geometric and Kolmogorov's axiomatic definition. It also covers conditional probability and Bayes's Theorem.
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