# ddmix: Density Functions of Mixture Models In EMMIXskew: The EM Algorithm and Skew Mixture Distribution

## Description

Calculate the density of multivariate mixture models at data points for each component

## Usage

 `1` ```ddmix( dat, n, p, g, distr, mu, sigma, dof=NULL, delta=NULL) ```

## Arguments

 `dat` The dataset `n` The total number of points `p` Dimension of data `g` The number of clusters `distr` A three letter string indicating the distribution; "mvn" for normal, "mvt" for t distribution, "msn" for skew normal, and "mst" for skew t distribution. `mu` A numeric mean matrix with each column corresponding to the mean `sigma ` An array of dimension (p,p,g) with first two dimensions corresponding covariance matrix of each component `dof ` A vector of degrees of freedom for each component `delta` A matrix with each column as skew parameter vector

## Value

ddmix gives an n by g matrix of logorithm of density at each data point for each component.

## References

McLachlan G.J. and Krishnan T. (2008). The EM Algorithm and Extensions (2nd). New Jersay: Wiley.

McLachlan G.J. and Peel D. (2000). Finite Mixture Models. New York: Wiley.

`ddmvn`,`ddmvt`,`ddmsn`,`ddmst`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```p=2 g=3 #mixing propotion of each component pro <- c(0.3,0.3,0.4) #specify mean and covariance matrix for each component sigma<-array(0,c(2,2,3)) for(h in 2:3) sigma[,,h]<-diag(2) sigma[,,1]<-cbind( c(1,0),c(0,.1)) mu <- cbind(c(4,-4),c(3.5,4),c( 0, 0)) #specify other parameters for "mvt","msn","mst" delta <- cbind(c(3,3),c(1,5),c(-3,1)) dof <- c(3,5,5) #specify the distribution distr <- "mst" y <- c(1,2) n=1 #then the density value at y for the mixture model is ddmix(y, n, p, g, distr, mu, sigma, dof, delta) ```