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Efficient dependency models: Simulating dependent random variables

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  • Lamboni, Matieyendou

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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  • Lamboni, Matieyendou, 2022. "Efficient dependency models: Simulating dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 199-217.
    • Handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:199-217
    DOI: 10.1016/j.matcom.2022.04.018
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    References listed on IDEAS

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    1. Frédéric Vrins, 2018. "Sampling the Multivariate Standard Normal Distribution under a Weighted Sum Constraint," Risks, MDPI, vol. 6(3), pages 1-13, June.
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    5. Lamboni, Matieyendou, 2019. "Multivariate sensitivity analysis: Minimum variance unbiased estimators of the first-order and total-effect covariance matrices," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 67-92.
    6. Rüschendorf, Ludger & de Valk, Vincent, 1993. "On regression representations of stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 183-198, June.
    7. Lamboni, Matieyendou & Kucherenko, Sergei, 2021. "Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    8. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, September.
    9. Lamboni, Matieyendou, 2020. "Derivative-based generalized sensitivity indices and Sobol’ indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 236-256.
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    Cited by:

    1. Matieyendou Lamboni, 2024. "Kernel-based Measures of Association Between Inputs and Outputs Using ANOVA," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 790-826, August.

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