| Title | Stabilne distribucije |
| Author | Matea Ivanešić |
| Mentor(s) | Nenad Šuvak (thesis advisor)
|
| 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. |
| Parallel title (English) | Stable distributions |
| Granter | Josip Juraj Strossmayer University of Osijek
Department of Mathematics |
| Lower level organizational units | Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group |
| Place | Osijek |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics |
| Study specialization | Financial and Statistical Mathematics |
| Academic title abbreviation | mag.math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2016 |
| Parallel 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. |
| Parallel keywords (Croatian) | stabilne distribucije slučajne varijable |
| Resource type | text |
| Access condition | Open access |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:126:145854 |
