mclustMarginalParams: Marginal parameters from fitted GMMs via mclust

In mclustAddons: Addons for the 'mclust' Package

Marginal parameters from fitted GMMs via mclust

Description

Function to compute the marginal parameters from a fitted Gaussian mixture models.

Usage

mclustMarginalParams(object, ...)

gmm2margParams(pro, mu, sigma, ...)

Arguments

object	An object of class Mclust or densityMclust.
...	Further arguments passed to or from other methods.
pro	A vector of mixing proportions for each mixture component.
mu	A matrix of mean vectors for each mixture component. For a d-variate dataset on G components, the matrix has dimension (d \times G).
sigma	An array of covariance matrices for each mixture component. For a d-variate dataset on G components, the array has dimension (d \times d \times G).

Details

Given a G-component GMM with estimated mixture weight \pi_k, mean vector \mu_{k}, and covariance matrix \Sigma_{k}, for mixture component k = 1, \dots, G, then the marginal distribution has:

• mean vector

  \mu = \sum_{k=1}^G \pi_k \mu_k

• covariance matrix

  \Sigma = \sum_{k=1}^G \pi_k \Sigma_k + \pi_k (\mu_k - \mu)'(\mu_k - \mu)

Value

Returns a list of two components for the mean and covariance of the marginal distribution.

Author(s)

Luca Scrucca

References

Frühwirth-Schnatter S. (2006) Finite Mixture and Markov Switching Models, Springer, Sec. 6.1.1

See Also

mclust::Mclust(), mclust::densityMclust().

Examples

x = iris[,1:4]
mod = Mclust(x, G = 3)
mod$parameters$pro
mod$parameters$mean
mod$parameters$variance$sigma
mclustMarginalParams(mod)

mclustAddons documentation built on April 3, 2025, 11:19 p.m.