Conditional quantile reproducibility of multivariate distributions and simplified pair copula construction

We give an equivalent definition of the conditional quantile reproducibility property for multivariate probability distributions using the concept of copula. Based on this definition, we establish a connection between the conditional quantile reproducibility property and the simplifying assumption from the simplified pair copula construction. Additionally, we show that the conditional quantile reproducibility is preserved when moving from a multivariate distribution to its copula.