Efficient dependency models for some distributions

TL;DR

This paper develops practical dependency functions for classical multivariate distributions, enhancing uncertainty quantification, sensitivity analysis, and simulation of dependent variables with efficient sampling methods.

Contribution

It introduces mathematically derived dependency functions for key distributions and proposes a method to select efficient sampling functions using multivariate sensitivity analysis.

Findings

Derived dependency functions for Dirichlet, elliptical, uniform, gamma, and Gaussian distributions.

Provided a systematic approach for choosing efficient sampling functions.

Validated the approach through numerical simulations.

Abstract

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.