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On Exact Distribution for Multivariate Weighted Distributions and Classification

Author

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  • Matieyendou Lamboni

    (University of Guyane
    University of Guyane, University of Réunion, IRD, University of Montpellier)

Abstract

We are interested in analyzing specific model behaviors such as the model output(s) values within a given cluster using the probability theory. By showing the relevance of the multivariate weighted distribution theory to characterize some behaviors of interest thanks to the weight functions, we derive the distribution function of the model inputs that complies with a specific model behavior (called target inputs distribution). The target inputs lead to the target output(s) using the model, including clustering outcomes of rule-based ensembles, random forest, kernel-based learning and fuzzy clustering. Two expressions of that distribution are provided, including the copula. Conditional moments of the target output(s) and dependency models of the target inputs are also derived for the purpose of uncertainty quantification and sensitivity analysis. For computing such quantities of interest, consistent estimators and detailed illustrations of our approach are provided, including a real case study.

Suggested Citation

  • Matieyendou Lamboni, 2023. "On Exact Distribution for Multivariate Weighted Distributions and Classification," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09993-2
    DOI: 10.1007/s11009-023-09993-2
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    References listed on IDEAS

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    1. Elja Arjas & Tapani Lehtonen, 1978. "Approximating Many Server Queues by Means of Single Server Queues," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 205-223, August.
    2. Lamboni, Matieyendou & Monod, Hervé & Makowski, David, 2011. "Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 450-459.
    3. Robert Eymard & Sophie Mercier & Michel Roussignol, 2011. "Importance and Sensitivity Analysis in Dynamic Reliability," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 75-104, March.
    4. Youngjun Choe & Henry Lam & Eunshin Byon, 2018. "Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1155-1172, December.
    5. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    6. 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).
    7. Ronald L. Iman & Stephen C. Hora, 1990. "A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis," Risk Analysis, John Wiley & Sons, vol. 10(3), pages 401-406, September.
    8. Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(4), pages 519-529, December.
    9. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
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