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Probabilities on Cones of Multimatrix Variate Distributions and Elliptical Affine Shape Distributions Under Real Normed Division Algebras

Author

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  • Francisco J. Caro-Lopera

    (Universidad de Medellín)

  • José A. Díaz-García

    (Universidad Autónoma de Chihuahua)

Abstract

This work proposes probabilities of multimatrix distributions and simplifies the affine shape theory under the setting of real normed division algebras and elliptically contoured laws. The contribution of the paper, valid for all real normed division algebras and elliptical distributions, involves: 1) computable probabilities for several matrices in multimatrix distributions; 2) computable probability for several multimatrix variate generalised Wishart distributions; 3) probability study of the multimatrix variate Pearson type II distribution; 4) a new setting for generalised estatistical shape theory; 5) a dynamic molecular docking based on matrix probabilities, under dependent samples of a reported inhibitor in two cavities of SARS-CoV-2.

Suggested Citation

  • Francisco J. Caro-Lopera & José A. Díaz-García, 2025. "Probabilities on Cones of Multimatrix Variate Distributions and Elliptical Affine Shape Distributions Under Real Normed Division Algebras," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(2), pages 349-377, August.
    • Handle: RePEc:spr:sankha:v:87:y:2025:i:2:d:10.1007_s13171-025-00402-z
    DOI: 10.1007/s13171-025-00402-z
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    References listed on IDEAS

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    1. Díaz-García, José A. & Caro-Lopera, Francisco J., 2016. "Elliptical affine shape distributions for real normed division algebras," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 139-149.
    2. Zhenming Jin & Xiaoyu Du & Yechun Xu & Yongqiang Deng & Meiqin Liu & Yao Zhao & Bing Zhang & Xiaofeng Li & Leike Zhang & Chao Peng & Yinkai Duan & Jing Yu & Lin Wang & Kailin Yang & Fengjiang Liu & Re, 2020. "Structure of Mpro from SARS-CoV-2 and discovery of its inhibitors," Nature, Nature, vol. 582(7811), pages 289-293, June.
    3. Caro-Lopera, Francisco J. & González-Farías, Graciela & Balakrishnan, N., 2013. "Determinants, permanents and some applications to statistical shape theory," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 29-39.
    4. Caro-Lopera, Francisco J. & Díaz-García, José A. & González-Farías, Graciela, 2010. "Noncentral elliptical configuration density," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 32-43, January.
    5. Caro-Lopera, Francisco J. & González Farías, Graciela & Balakrishnan, Narayanaswamy, 2016. "Matrix-variate distribution theory under elliptical models-4: Joint distribution of latent roots of covariance matrix and the largest and smallest latent roots," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 224-235.
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