MixSAL (version 1.0)

dsal: Probability Density Function for a Multivariate SAL Distribution

Description

Evaluates the probability density function of a multivariate SAL distribution.

Usage

dsal(x, alpha, sig, mu)

Arguments

x

A n by p matrix where each row corresponds a p-dimensional observation.

alpha

A vector specifying the direction of skewness in each variable.

sig

A matrix specifying the covariance matrix of the variables.

mu

A vector specifiying the mean vector.

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.

Kotz et. al (2001). The Laplace Distribution and Generalizations: A Revisit with Applications to Communications. Economics, Engineering, and Finance. 1st Edition, Burkhauser.

Examples

# NOT RUN {
## For this illustration, consider bivariate SAL data from the specified distribution:
x <- rsal(n=10,p=2,alpha=c(2,2),sig=diag(2),mu=c(0,0))
## The value of the probability density function for each of the simulated values are given by:
dsal(x=x,alpha=c(2,2),sig=diag(2),mu=c(0,0))
# }