multvardiv-package

Tools for Multivariate Probability Distributions

This package provides tools for multivariate probability distributions:

• Multivariate generalized Gaussian distribution (MGGD)
• Multivariate Cauchy distribution (MCD)
• Multivariate $t$ distribution (MTD) package

Details

For each of these probability distributions, are provided:

• Calculation of distances/divergences between two distributions:

  • Renyi divergence, Bhattacharyya distance, Hellinger distance (for now, only available for the $t$ distribution): diststudent
  • Kullback-Leibler divergence: kld

• Tools for these probability distributions: probability distribution function, parameter estimation, sample estimation

  • MGGD: dmggd, estparmggd, rmggd
  • MCD: dmcd, estparmcd, rmcd
  • MTD: dmtd, estparmtd, rmtd
  • Plot of the density of a distribution with 2 variables: plotmvd, contourmvd

References

N. Bouhlel, A. Dziri, Kullback-Leibler Divergence Between Multivariate Generalized Gaussian Distributions. IEEE Signal Processing Letters, vol. 26 no. 7, July 2019. tools:::Rd_expr_doi("10.1109/LSP.2019.2915000")

N. Bouhlel, D. Rousseau, A Generic Formula and Some Special Cases for the Kullback–Leibler Divergence between Central Multivariate Cauchy Distributions. Entropy, 24, 838, July 2022. tools:::Rd_expr_doi("10.3390/e24060838")

N. Bouhlel and D. Rousseau (2023), Exact Rényi and Kullback-Leibler Divergences Between Multivariate t-Distributions, IEEE Signal Processing Letters. tools:::Rd_expr_doi("10.1109/LSP.2023.3324594")

See Also

Useful links:

• https://forgemia.inra.fr/imhorphen/multvardiv
• Report bugs at https://forgemia.inra.fr/imhorphen/multvardiv/-/issues

Author(s)

Pierre Santagostini pierre.santagostini@institut-agro.fr, Nizar Bouhlel nizar.bouhlel@institut-agro.fr, nizar.bouhlel@inrae.fr