Kopule in asimetrija parov slučajnih spremenljiv

Kopule so v zadnjem času postale uporabne predvsem za proučevanje odvisnosti in korelacije slučajnih spremenljivk, dodatno pa omogočajo tudi modeliranje porazdelitev slučajnih vektorjev preko ocen za njihove robne porazdelitve. V tem članku so predstavljeni osnovni koncepti teorije kopul, nato pa je vpeljan tudi pojem asimetrije parov slučajnih spremenljivk. V zadnjem delu sledi še obravnava različnih razredov kopul glede na pripadajočo zgornjo mejo asimetrije.

Copulas and asymmetry of pairs of random variables

Recently copulas have become useful mainly for the study of the dependence and correlation of random variables, but additionally they allow for modelling of distributions of random vectors via estimates for their marginal distributions. In this article, the basic concepts of Copula theory are summarised, followed by the introduction of the notion of asymmetry of pairs of random variables. In the final part, different classes of copulas are examined according to their upper limit of asymmetry.