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Kopule v modelih udarov : delo diplomskega seminarja
ID Gubanec Hančič, Matija (Author), ID Kokol-Bukovšek, Damjana (Mentor) More about this mentor... This link opens in a new window, ID Mojškerc, Blaž (Co-mentor)

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Abstract
V delu predstavimo kopule in njihovo uporabo v modelih udarov. Ime kopula izvira iz latinske besede za 'vez' ali 'povezavo', kar v grobem tudi opiše njihov namen. Kopule definiramo in prek Sklarovega izreka vpeljemo v svet verjetnosti in porazdelitvenih funkcij. Za lažjo predstavo se srečamo z bolj znanimi kopulami in jih vizualno predstavimo v obliki prostorskih grafov, nivojnic in razsevnih diagramov. Vpeljemo jih v modele udarov in na primerih prikažemo njihovo uporabno vrednost. Z modeli udarov predstavimo prihod udara v nek sistem. Glede na vrsto in porazdelitev časov udarov ter število in vrsto komponent razlikujemo različne modele. V tem delu se bomo srečali z dvokomponentnimi sistemi in glede na učinek in porazdelitev časov udarov ločili tri primere. Za različne modele udarov definiramo kopule in z njihovo pomočjo povežemo porazdelitvene funkcije življenjskih dob v porazdelitveno funkcijo življenjske dobe sistema.

Language:Slovenian
Keywords:kopule, modeli udarov, Marshallova kopula, maksmin kopula, Marshall-Olkinova kopula, analiza preživetja, nivojnice, razsevni diagrami
Work type:Final seminar paper (mb14)
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
UDC:519.2
COBISS.SI-ID:18821721 This link opens in a new window
Publication date in RUL:19.09.2019
Views:664
Downloads:210
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Secondary language

Language:English
Title:Copulas in shock models
Abstract:
We introduce copulas and their usage in shock models. The name copula derives from the latin word for 'link' or 'tie', which roughly describes their purpose. We define copulas and introduce them to the world of probability and distribution functions via the Sklar theorem. To get a clearer picture of what copulas are, we get to know some of the more famous copulas and see their visual representations in the form of spatial graphs, contour plots and scatterplots. We introduce copulas to shock models and show their usability via examples. Via shock models we introduce arrivals of shocks into systems. Based on the type and distribution of shock arrival times and number and types of components we distinguish different models. In this thesis we will get acquintanced with two-component systems, and based on effects and the distribution of shock arrival times we will define three different models. We define copulas for different shock models and through their application bind multiple univariate distribution functions into one distribution function of the system.

Keywords:copulas, shock models, Marshall copula, maxmin copula, Marshall-Olkin copula, survival analysis, contour plots, scatterplots

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