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# Article

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Keywords:
\$d\$-copulas; fractal copulas; sample \$d\$-copulas of order \$m\$
Summary:
In this paper we analyze the construction of \$d\$-copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample \$d\$-copula of order \$m\$ with \$m≥2\$, the central idea is to use the above methodologies to construct a new copula based on a sample. The greatest advantage of the sample \$d\$-copula is the fact that it is already an approximating \$d\$-copula and that it is easily obtained. We will see that these new copulas provide a nice way to study multivariate data with an approximating copula which is simpler than the empirical multivariate copula, and that the empirical copula is the restriction to a grid of a sample \$d\$-copula of order \$n\$. These sample \$d\$-copulas can be used to make statistical inference about the distribution of the data, as shown in Section 3.
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