In this paper we give an alternative proof of the construction of n-dimensional ordinal sums given in Mesiar and Sempi \cite{mesiar}, we also provide a new methodology to construct n-copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in \cite{durante08} and \cite{durante09}. Finally, we use the gluing method of Siburg and Stoimenov \cite{siburg} and its generalization in Mesiar {et al.} \cite{mesiarjagr} to give an alternative method of patchwork construction of n-copulas, which can be also used in composition with our patchwork method.
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≥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.