Efficient dependency models for some distributions

2022/03/17 by Matieyendou Lamboni, Lamboni, Matieyendou
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #math.PR #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.2203.10092

arxiv created 2022/03/17 · arxiv updated 2022/03/22

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.

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