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master's thesis
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Stable distributions
Matea Ivanešić (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Cite this document

Ivanešić, M. (2016). Stabilne distribucije (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:145854

Ivanešić, Matea. "Stabilne distribucije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:145854

Ivanešić, Matea. "Stabilne distribucije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:145854

Ivanešić, M. (2016). 'Stabilne distribucije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 24 January 2020, https://urn.nsk.hr/urn:nbn:hr:126:145854

Ivanešić M. Stabilne distribucije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2020 January 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:145854

M. Ivanešić, "Stabilne distribucije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:145854

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Metadata
TitleStabilne distribucije
Title (english)Stable distributions
AuthorMatea Ivanešić
MentorNenad Šuvak (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2016, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Cilj ovog diplomskog rada je upoznavanje sa stabilnim distribucijama i strukturama zavisnosti stabilnih distribucija. U radu smo se bavili stabilnim distribucijama slučajnih varijabli, a zatim slučajnih vektora. Na početku smo se upoznali sa stabilnim distribucijama slučajnih varijabli te denirali kada su te distribucije simetrične stabilne, odnosno strogo stabilne. Naveli smo i dokazali neka svojstva stabilnih distribucija. Dalje smo se bavili stabilnim distribucijama slučajnih vektora te uveli pojmove poput kovarijacije, kovarijacijske norme, Jamesove ortogonalnosti, kodiferentnosti,α- slučajne mjere te prikaza slučajnih varijabli preko integrala. Na kraju smo proučavali strukture zavisnosti stabilnih distribucija. Gledali smo poveznicu stabilnih distribucija i linearne regresije, simetričnih uvjetnih distribucija, linearne ovisnosti, momenta slučajnog vektora i asociranosti slučajnih varijabli.
Abstract (english)
The aim of this diploma thesis is to introduce stable distributions and dependence structures of multivariate stable distributions. In the beginning we introduced stable distributions of random variables and dened symmetric stable and strictly stable distributions. We stated and proved some properties of stable distributions. Moreover, we were dealing with stable distributions of random vectors and we introduced some new terms like covariation, covariation norm, James orthogonality, codierence, α-stable random measure and integral representation of random variables. In the end we were studying dependence structures of multivariate stable distributions. Furthermore, the relation between stable distributions and linear regression, symmetric conditional laws, linear dependence, joint moments and association of random variables were analysed.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:126:145854
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2016-04-07 08:25:22