dmsn: Multivariate skew-normal distribution

Description

Probability density function and random number generation for the multivariate skew-normal (MSN) distribution.

Usage

dmsn(x, xi=rep(0,k), Omega, alpha)
rmsn(n=1, xi=rep(0,k), Omega, alpha)

Arguments

either a vector of length k or a matrix with k columns, where k is length(alpha), giving the coordinates of the point(s) where the density must be avaluated.

Omega

a covariance matrix of dimension (k,k).

alpha

a numeric vector which regulates the shape of the density.

a numeric vector of lenght k, or a matrix with k columns, representing the location parameter of the distribution. If xi is a matrix, its dimensions must agree with those of x.

a numeric value which represents the number of random vectors to be drawn.

Value

A vector of density values (dmsn), or a matrix of random points (rmsn).

Background

The multivariate skew-normal distribution is discussed by Azzalini and Dalla Valle (1996); the (Omega,alpha) parametrization adopted here is the one of Azzalini and Capitanio (1999).

References

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715--726.

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

Examples

Run this code

x <- seq(-3,3,length=30)
pdf <- dmsn(cbind(x,0), c(0,0), diag(2), c(2,3))
#
rnd <- rmsn(50,  c(0,0), diag(2), c(2,3))

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