  Dependency functions of dependent variables are relevant for i) performing
uncertainty quantification and sensitivity analysis in presence of dependent
variables and/or correlated variables, and ii) simulating random dependent
variables. In this paper, we mathematically derive practical dependency
functions for classical multivariate distributions such as Dirichlet,
elliptical distributions and independent uniform (resp. gamma and Gaussian)
variables under constraints that are ready to be used. Since such dependency
models are used for sampling random values and we have many dependency models
for every joint cumulative distribution function, we provide a way for choosing
the efficient sampling function using multivariate sensitivity analysis. We
illustrate our approach by means of numerical simulations.
