What are copulas?
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CitationMardani-Fard, H. A. ve Ardalan, A. (2009). What are copulas?. Maltepe Üniversitesi. s. 195.
A copula is, in fact, a multivariate distribution function with standard uniform margins. Sklar (1959) proved that for a d−variate distribution function F with univariate margins F1, . . . , Fd, there exists a d−copula, CF , such that F (x) = F (x1, . . . , xd) = CF (F (x1), . . . , F (xd)), for all x ∈ R d . Studying multivariate distribution functions with given margins coincides with studying copulas. For example, looking for bounds on a specified class of multivariate distribution functions with given margins coincides with trying to find bounds on a class of copulas with related conditions. Also,CF can be stand for the joint information of F , against its marginal information (that are all in its marginal distribution functions). As a result, in the studying of association of two random variables, it is useful to restrict our attentions to the copula-based measures. In this work we give some interpretations and properties of copulas and present some ways to construct a copula. Also, some applications of copulas were presented. In many parts of this work, the particular case d = 2 is discussed.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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