Μοντελοποίηση τυχαίων εξαρτημένων μεταβλητών μέσω copulas : οι εφαρμογές τους στη στατιστική
Αρφάνης, Γεώργιος Σ.
Copulas are one of the most frequently discussed issues in statistical science with many applications, particularly in finance. Their wide use is based on the fact that they connect multidimensional distribution functions, with their respective one-dimensional marginals.In this paper, a more theoretical approach of copulas and their properties is given, which starts with a throwback. Then we give analytical definitions and copula properties such as Sklar’s theorem and the concept of dependence between random variables. We continue by analyzing some copula classes such as the Marshal-Olkin, the elliptical copulas and the Archimedean copulas which are more thoroughly examined because of their variety, the number of applications they have and the ease of simulating copula families in this class. As a next step we present some parametric and non-parametric methods for estimating copulas and ways of choosing the right copula. Finally we give simulation algorithms and two very important applications of copulas in statistics.