R: Density of (Mixture) Multivariate Normal Distribution

MVN {EMCluster} | R Documentation

## Density of (Mixture) Multivariate Normal Distribution

### Description

These functions are tools for compute density of (mixture) multivariate Gaussian distribution with unstructured dispersion.

### Usage

    dmvn(x, mu, LTsigma, log = FALSE)
    dlmvn(x, mu, LTsigma, log = TRUE)
    dmixmvn(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL, log = FALSE)
    logL(x, emobj = NULL, pi = NULL, Mu = NULL, LTSigma = NULL)

### Arguments

`x` | the data matrix, dimension n * p.
`mu` | the centers of clusters, length p.
`LTsigma` | the lower triangular matrices of dispersion, length p(p+1)/2.
`log` | if logarithm returned.
`emobj` | the desired model which is a list mainly contains `pi`, `Mu`, and `LTSigma`, usually a returned object from `init.EM`.
`pi` | the mixing proportion, length K.
`Mu` | the centers of clusters, dimension K * p.
`LTSigma` | the lower triangular matrices of dispersion, K * p(p+1)/2.

### Details

The `dmvn` and `dlmvn` compute density and log density of multivariate distribution.

The `dmixmvn` computes density of mixture multivariate distribution and is based either an input `emobj` or inputs `pi`, `Mu`, and `LTSigma` to assign class id to each observation of `x`.

The `logL` returns the value of the observed log likelihood function of the parameters at the current values of the parameters `pi`, `Mu`, and `LTSigma`, with the suplied data matrix `x`.

### Value

A density value is returned.

### Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

### References

https://www.stat.iastate.edu/people/ranjan-maitra

### See Also

`init.EM`, `emcluster`.

### Examples

    library(EMCluster, quietly = TRUE)
    x2 <- da2$da
    x3 <- da3$da

    emobj2 <- list(pi = da2$pi, Mu = da2$Mu, LTSigma = da2$LTSigma)
    emobj3 <- list(pi = da3$pi, Mu = da3$Mu, LTSigma = da3$LTSigma)

    logL(x2, emobj = emobj2)
    logL(x3, emobj = emobj3)

    dmixmvn2 <- dmixmvn(x2, emobj2)
    dmixmvn3 <- dmixmvn(x3, emobj3)

    dlmvn(da2$da[1,], da2$Mu[1,], da2$LTSigma[1,])
    log(dmvn(da2$da[1,], da2$Mu[1,], da2$LTSigma[1,]))

[Package EMCluster version 0.2-13 Index]