20.500.12556/RUL-140055 Uporaba kopul pri modeliranju odvisnosti diskretnih slučajnih vektorjev delo diplomskega seminarja Use of copulas in modeling dependance between discrete random vectors Ko želimo kopule uporabiti za modeliranje diskretno porazdeljenih slučajnih vektorjev, naletimo na številne težave. Ena od njih je odsotnost enoličnosti, ki bo vodila v nejasnosti, s kakšnimi objekti imamo opravka. To težavo bomo kvantificirali preko vpeljave kopul spodnje in zgornje Carleyine meje ter njunih mer skladnosti in posebej preko funkcije splošcenosti mej. Vrednost kopule in vrednost kopuline mere skladnosti je vsebovana na intervalu med vrednostima Carleyinih mej. Za zvezne slučajne spremenljivke med vrednostmi mer skladnosti, kopulami in funkcijskimi odvisnostmi veljajo ekvivalenčne relacije, kar pa se v diskretne primere ne prenese, relacije se navadno ohranijo le v eno od smeri. To bomo prikazali z konkretnimi zgledi. Eden od razlogov za probleme, ki v diskretnih primerih nastopajo, je neničelna verjetnost enakih izidov, kar bomo poskusili popraviti preko vpeljave modificiranih mer skladnosti. Navedli bomo nekaj odvisnostnih lastnosti, ki se bodo iz kopulskih modelov prenesli na odvisnost med slučajnimi spremenljivkami, kar bo pokazalo, da kopule tudi v diskretnih primerih še vedno ostajajo uporabne. Na simulacijah bomo prikazali težave ocenjevanja parametra odvisnosti preko mer skladnosti. When we try to use copulas for modeling discretely distributed random vectors, we encounter quite a few problems. One of them is the lack of uniqueness, which leads into confusion about what sort of objects we are dealing with. The problem of unidentifiability will be quantified by introducing two copulas known as Carley’s bounds and their measures of concordance and separately as a function of the flatness of the margins. The values of copulas derived form discrete cases and the values of their measures of concordance are contained inside the intervals of Carley’s bounds and measures of the bounds respectively. In continuous cases we have equivalence relations between copulas, measures of concordance and functional dependencies, but sadly many of them do not translate into discrete ones and some hold only one way. This will be shown through examples. One of the reasons for difficulties in discrete cases arises from non-zero probability of encountering ties, which we’ll try to correct by introducing modified concordance measures. We will list some of the dependency relations that do in fact translate from copulas into discretely distributed random vectors. They will show us, that even when dealing with discrete distributions, copulas still retain some of their use. We’ll use simulations to demonstrate the before mentioned problems and problems of estimating the dependance parameter. Kendallov tau kopula Sklarov izrek skladnost Spearmannov ro Kendall’s tau copula Sklar’s theorem concordance Spearmann’s rho true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2022-09-10 08:15:04 2022-09-10 08:15:07 2024-05-29 12:11:38 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 126809 120958467 5295.pdf 5295.pdf 1 6808F79724079248406476932F852E50 52c1f40620087f1664003a5e61f8092ddaee119eb2e070892fe38cad4b43c731 dc2e04d8-30cf-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=160720 Fakulteta za matematiko in fiziko 0 0 0