# dmsal: Probability Density Function for a Mixture of SAL... In MixSAL: Mixtures of Multivariate Shifted Asymmetric Laplace (SAL) Distributions

## Description

Evaluates the probability density function of a mixture of multivariate SAL distribution.

## Usage

 `1` ```dmsal(x, alpha, sig, mu, pi.g) ```

## Arguments

 `x` A n by p matrix where each row corresponds a p-dimensional observation. `alpha` A matrix where each row specifies the direction of skewness in each variable for each mixture component. `sig` An array where each matrix specifies the covariance matrix for each mixture component. `mu` A matrix where each row gives the mean vector for each mixture component. `pi.g` A vector specifying the mixing components.

## Value

A vector of length n that gives the value of the probability density function for each observation in the matrix x and the specified parameter values.

## Author(s)

Brian C. Franczak [aut, cre], Ryan P. Browne [aut, ctb], Paul D. McNicholas [aut, ctb]

Maintainer: Brian C. Franczak <[email protected]>

## References

Franczak et. al (2014). Mixtures of Shifted Asymmetric Laplace Distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(6), 1149-1157.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## For this illustration, consider the following dataset generated from a mixture of bivariate SAL ##distributions with the specified parameter set: alpha <- matrix(c(2,2,1,2),2,2) sig <- array(NA,dim=c(2,2,2)) sig[,,1] <- diag(2) sig[,,2] <- matrix(c(1,0.5,0.5,1),2,2) mu <- matrix(c(0,0,-2,5),2,2) pi.g <- rep(1/2,2) x <- rmsal(n=10,p=2,alpha=alpha,sig=sig,mu=mu,pi.g=pi.g) ## The value of the probability density function for each of the simulated values are given by: dmsal(x=x[,-1],alpha=alpha,sig=sig,mu=mu,pi.g=pi.g) ```

MixSAL documentation built on May 18, 2018, 5:04 p.m.