## New families of copulas based on periodic functions.(English)Zbl 1071.62047

The purpose of this paper is to introduce new families of copulas, for the 2- and n-dimensional case functions, using three characteristic properties of copulas and a procedure based on periodic functions. Section 2 defines and studies the new copula functions for bivariate dependence. Section 3 considers a bivariate family of smooth periodic copulas attaining for Frechét bounds and independence. Section 4 extends the proposed copula construction technique from the bivariate case to the $$n$$-dimensional framework, providing families of copulas in dimension $$n$$ and parameterized by $$(n - 1)$$ parameters, which imply possibly asymmetric relations. There is explained how periodic copulas that admit density functions can be simulated.

### MSC:

 62H05 Characterization and structure theory for multivariate probability distributions; copulas 60E05 Probability distributions: general theory 62H10 Multivariate distribution of statistics 62P05 Applications of statistics to actuarial sciences and financial mathematics 65C60 Computational problems in statistics (MSC2010)
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### References:

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