The need for a method to construct multidimensional distribution function is increasing recently , in the era of huge multiwavelength surveys .
We have proposed a systematic method to build a bivariate luminosity or mass function of galaxies by using a copula ( 67 ) .
It allows us to construct a distribution function when only its marginal distributions are known , and we have to estimate the dependence structure from data .
A typical example is the situation that we have univariate luminosity functions at some wavelengths for a survey , but the joint distribution is unknown .
Main limitation of the copula method is that it is not easy to extend a joint function to higher dimensions ( d > 2 ) , except some special cases like multidimensional Gaussian .
Even if we find such a multivariate analytic function in some fortunate case , it would often be inflexible and impractical .
In this work , we show a systematic method to extend the copula method to unlimitedly higher dimensions by a vine copula .
This is based on the pair-copula decomposition of a general multivariate distribution .
We show how the vine copula construction is flexible and extendable .
We also present an example of the construction of an stellar mass–atomic gas–molecular gas 3-dimensional mass function .
We demonstrate the maximum likelihood estimation of the best functional form for this function , as well as a proper model selection via vine copula .