MixSAL (version 1.0)

dmsal: Probability Density Function for a Mixture of SAL Distributions

Description

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

Usage

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.

References

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

Examples

# NOT RUN {
## 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)
# }