Kybernetika 49 no. 5, 663-691, 2013

Sample d-copula of order m

José M. González-Barrios and María M. Hernández-Cedillo


In this paper we analyze the construction of $d$-copulas including the ideas of Cuculescu and Theodorescu \cite{cucutheo}, Fredricks et al. \cite{frenero}, Mikusiński and Taylor \cite{mitay} and Trutschnig and Fernández-Sánchez \cite{trutfer}. 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 $m\geq 2$, 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.


$d$-copulas, fractal copulas, sample $d$-copulas of order $m$


60A10, 60E05, 62E10


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