  Multivariate datasets are common in various real-world applications.
Recently, copulas have received significant attention for modeling dependencies
among random variables. A copula-based information measure is required to
quantify the uncertainty inherent in these dependencies. This paper introduces
a multivariate variant of the cumulative copula entropy and explores its
various properties, including bounds, stochastic orders, and
convergence-related results. Additionally, we define a cumulative copula
information generating function and derive it for several well-known families
of multivariate copulas. A fractional generalization of the multivariate
cumulative copula entropy is also introduced and examined. We present a
non-parametric estimator of the cumulative copula entropy using empirical beta
copula. Furthermore, we propose a new distance measure between two copulas
based on the Kullback-Leibler divergence and discuss a goodness-of-fit test
based on this measure.
