20.500.12556/RUL-165325 Ekstremni volumni kvazi-kopul Extreme volumes of quasi-copulas Diplomska naloga obravnava problem iskanja ekstremnih volumnov kvazi-kopul, ki so posplošene oblike kopul in se uporabljajo za modeliranje odvisnosti med večdimenzionalnimi slučajnimi spremenljivkami. Ekstremni volumni kvazi-kopul so kvantitativno merilo, koliko se lahko kvazi-kopule razlikujejo od kopul. Osredotočimo se na iskanje ekstremnih volumnov za višje dimenzije s pristopom linearnega programiranja. Izpeljani linearni program rešujemo z metodo simpleksov in metodo notranje točke v programu Mathematica in Matlab ter primerjamo dobljene rezultate. Izkaže se, da domneva za izračun spodnje meje volumna v članku iz 2023 ne drži. Ekstremni volumni, pridobljeni z metodo simpleksov v Mathematici, so v obliki racionalnih števil in lahko prispevajo k možnosti za določitev točne formule za ekstremne volumne kvazi-kopul. This thesis addresses the problem of finding the extreme volumes of quasi-copulas, which are generalized forms of copulas used to model dependencies between multidimensional random variables. The extreme volumes of quasi-copulas provide a quantitative measure of how much quasi-copulas can differ from copulas. We focus on finding extreme volumes for higher dimensions using the approach of linear programming. The derived linear program is solved using the simplex method and the interior-point method in Mathematica and Matlab, and the obtained results are compared. It turns out that the conjecture for calculating the lower bound of the volume in the 2023 article does not hold. The extreme volumes, obtained using the simplex method in Mathematica, are in the form of rational numbers and may contribute to the possibility of determining an exact formula for the extreme volumes of quasi-copulas. kopula kvazi-kopula ekstremni volumni linearno programiranje metoda simpleksov metoda notranje točke copula quasi-copula extreme volumes linear programming simplex method interior-point method true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-12-02 11:55:10 2024-12-02 11:55:10 2024-12-30 08:08:22 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37420 212934403 Belsak_Matej_-_Ekstremni_volumni_kvazi-kopul.pdf Belsak_Matej_-_Ekstremni_volumni_kvazi-kopul.pdf 1 08D7254A738A46EE2FF223564EA1DCE7 f796d74f21a6a16eebfcd2b8b014da214784f429e4840c85317273a55c6de676 786bdcea-b09b-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=196425 Fakulteta za računalništvo in informatiko 0 0 0