1,209 research outputs found
Náhodné procesy v analýze spolehlivosti
No full textNázev práce: Náhodné procesy v analýze spolehlivosti Autor: Kamil Chovanec Katedra: Katedra pravděpodobnosti a matematické statistiky Vedoucí diplomové práce: Doc. Petr Volf, CSc. e-mail vedoucího: [email protected] Abstrakt: Práce je zaměřena na analýzu spolehlivosti se zvláštním důrazem na Aalenův aditivní model. Při testování hypotéz v analýze spolehlivosti často získáváme proces, který za platnosti hypotézy konverguje ke Gaus- sovskému martingalu, jehož rozptyl umíme odhadnout rovnoměrně konzis- tentním odhadem. Dostáváme se tak vlastně k nové hypotéze o procesu získaném testováním původní hypotézy. Existuje více způsobů, jak tuto hy- potézu testovat. V práci jsou představeny některé z nich a síla těchto testů je pomocí Monte Carlo simulací porovnána pro různé modely a velikosti výběrového souboru. Ve speciálním případě je odvozen bod, který maxima- lizuje asymptotickou sílu dvou testů. Klíčová slova: Martingal, Aalenův aditivní model, riziková funkce 1Title: Random Processes in Reliability Analysis Author: Kamil Chovanec Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Supervisor's e-mail address: [email protected] Abstract: The thesis is aimed at the reliability analysis with special em- phasis at the Aalen additive model. The result of hypothesis testing in the reliability analysis is often a process that converges to a Gaussian martingale under the null hypothesis. We can estimate the variance of the martingale using a uniformly consistent estimator. The result of this estimation is a new hypothesis about the process resulting from the original hypothesis. There are several ways to test for this hypothesis. The thesis presents some of these tests and compares their power for various models and sample sizes using Monte Carlo simulations. In a special case we derive a point that maximizes the asymptotic power of two of the tests. Keywords: Martingale, Aalen's additive model, hazard function 1Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Random Processes in Reliability Analysis
No full textTitle: Random Processes in Reliability Analysis Author: Kamil Chovanec Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Supervisor's e-mail address: [email protected] Abstract: The thesis is aimed at the reliability analysis with special em- phasis at the Aalen additive model. The result of hypothesis testing in the reliability analysis is often a process that converges to a Gaussian martingale under the null hypothesis. We can estimate the variance of the martingale using a uniformly consistent estimator. The result of this estimation is a new hypothesis about the process resulting from the original hypothesis. There are several ways to test for this hypothesis. The thesis presents some of these tests and compares their power for various models and sample sizes using Monte Carlo simulations. In a special case we derive a point that maximizes the asymptotic power of two of the tests. Keywords: Martingale, Aalen's additive model, hazard function
Možnosti se stabilními distribucemi
No full textNázev práce: Možnosti se stabilními distribucemi. Autor: Andrea Karlová Katedra: Katedra pravděpodobnosti a matematické statistiky Vedoucí disertační práce: Doc. Petr Volf, CSc. Abstrakt: Stabilní rozdělení jsou úzce spojena s problematikou konvergence součtu nekonečných řad nezávislých náhodných veličin. Hustoty těchto pravděpodobnostních rozdělení jsou dobře zkoumána za použití integralních transformací. Nejprve shrneme známé výsledky odvozené pomocí Fourierovi transformace, dále se zaměříme na méně častou Mellinovu transformaci. Pomocí této budeme vyšetřovat rozdělení součinu dvou nezávislých stabilních náhodných veličin. Ve čtvrté kapitole zobecníme model Louise Bacheliera za pomoci stabilních rozdělení a budeme diskutovat prak- tické aspekty spojené s finančními deriváty. Klíčová slova: stabilní rozdělení, Mellinova transformace, součin nezávislých náhodných veličin, levy model, samoshodné plochy implikovaných volatilit 1Title: Options under Stable Laws. Author: Andrea Karlová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Abstract: Stable laws play a central role in the convergence problems of sums of independent random variables. In general, densities of stable laws are represented by special functions, and expressions via elementary functions are known only for a very few special cases. The convenient tool for investigating the properties of stable laws is provided by integral transformations. In particular, the Fourier transform and Mellin transform are greatly useful methods. We first discuss the Fourier transform and we give overview on the known results. Next we consider the Mellin transform and its applicability on the problem of the product of two independent random variables. We establish the density of the product of two independent stable random variables, discuss the properties of this product den- sity and give its representation in terms of power series and Fox's H-functions. The fourth chapter of this thesis is focused on the application of stable laws into option pricing. In particular, we generalize the model introduced by Louise Bachelier into stable laws. We establish the option pricing formulas under this model, which we refer to as the Lévy Flight...Matematicko-fyzikální fakultaFaculty of Mathematics and Physic
Options under Stable Laws
No full textTitle: Options under Stable Laws. Author: Andrea Karlová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Abstract: Stable laws play a central role in the convergence problems of sums of independent random variables. In general, densities of stable laws are represented by special functions, and expressions via elementary functions are known only for a very few special cases. The convenient tool for investigating the properties of stable laws is provided by integral transformations. In particular, the Fourier transform and Mellin transform are greatly useful methods. We first discuss the Fourier transform and we give overview on the known results. Next we consider the Mellin transform and its applicability on the problem of the product of two independent random variables. We establish the density of the product of two independent stable random variables, discuss the properties of this product den- sity and give its representation in terms of power series and Fox's H-functions. The fourth chapter of this thesis is focused on the application of stable laws into option pricing. In particular, we generalize the model introduced by Louise Bachelier into stable laws. We establish the option pricing formulas under this model, which we refer to as the Lévy Flight..
Regresní modely v analýze přežití a spolehlivosti
No full textRegression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data. 1Regresní modely v analýze přežití a spolehlivosti Disertační práce Petr Novák Univerzita Karlova v Praze, Matematicko-fyzikální fakulta Abstrakt: V předložené práci studujeme metody pro modelování závislosti dat z oblasti analýzy přežití a spolehlivosti na dostupných vysvětlujících proměnných. V první části práce studujeme základní modely analýzy přežití, porovnáváme vlastnosti Coxova modelu proporcionálního rizika, Aalenova aditivního modelu a modelu zrychleného času. Uvádíme metody pro testování dobré shody modelu s daty, založené na teorii čítacích procesů a martingalů, umožňující rozpoznat, který model popisuje data nejlépe. Druhá část se věnuje modelování opravitelných systémů. Studujeme způsoby, jak do modelů zahrnout informace o historii zařízení, včetně vlivu oprav a preventivní údržby. Užití představených metod předvádíme na příkladech z praxe a na simulo- vaných datech zkoumáme jejich chování v různých situacích. 1Katedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Regression models in survival analysis and reliability
No full textRegression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data.
Jubilees and news
No full textsummary:Netuka, Ivan; Veselý, Jiří: Sedmdesátiny profesora Jana Maříka.
Volf, Ivo: 21. mezinárodní fyzikální olympiáda.
Volf, Petr: Tradice pražské konference o teorii informace pokračuje
Jubilees and news
No full textsummary:Netuka, Ivan; Veselý, Jiří: Sedmdesátiny profesora Jana Maříka.
Volf, Ivo: 21. mezinárodní fyzikální olympiáda.
Volf, Petr: Tradice pražské konference o teorii informace pokračuje
Regression models for intensities of failures in the reliability analysis
No full textIn the present work we study regression models in reliability analysis. We compare the Cox proportional hazards model, Aalen additive model, accelerated failure time model and their combinations. For each model we present procedures for estimating parametric and non-parametric risk function parts and goodness-of-fit tests based on classic regression routines and counting process theory. We demonstrate those tests on both real and simulated data and we focus on procedures how to find the model with the best fit
Regression models for intensities of failures in the reliability analysis
No full textIn the present work we study regression models in reliability analysis. We compare the Cox proportional hazards model, Aalen additive model, accelerated failure time model and their combinations. For each model we present procedures for estimating parametric and non-parametric risk function parts and goodness-of-fit tests based on classic regression routines and counting process theory. We demonstrate those tests on both real and simulated data and we focus on procedures how to find the model with the best fit
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