Multivariate Generalized Gaussian Distribution, Multivariate t Distribution, Multivariate Cauchy Distribution, Statistical Divergence

Multivariate generalized Gaussian distribution, Multivariate Cauchy distribution, Multivariate t distribution. Distance between two distributions (see N. Bouhlel and A. Dziri (2019): , N. Bouhlel and D. Rousseau (2022): , N. Bouhlel and D. Rousseau (2023): ). Manipulation of these multivariate probability distributions. This package replaces 'mggd', 'mcauchyd' and 'mstudentd'.

multvardiv

The multvardiv packages replaces the mggd, mcauchyd and mstudentd packages.

This package provides tools for multivariate probability distributions:

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

For each of these probability distributions, some functions are available to compute the divergence between two distributions:

• Renyi, Bhattacharyya and Hellinger divergence
• Kullback-Leibler divergence

And some functions for the manipulation of probability distributions:

• Probability density
• Parameter estimation
• Sample simulation
• Density plot (bivariate distribution)

Installation

Install the package from CRAN:

install.packages("multvardiv")

Or install the development version from the repository, using the devtools package:

install.packages("devtools")
devtools::install_git("https://forge.inrae.fr/imhorphen/multvardiv")

Authors

Pierre Santagostini and Nizar Bouhlel

Reference

N. Bouhlel, A. Dziri, Kullback-Leibler Divergence Between Multivariate Generalized Gaussian Distributions. IEEE Signal Processing Letters, vol. 26 no. 7, July 2019. https://doi.org/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. https://doi.org/10.3390/e24060838

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