Multivariate skew-normal distribution

Usage

dmsn(x, xi, Omega, alpha)
rmsn(n, xi, Omega, alpha)

Arguments

x 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.
xi 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 (defaults is zeros(1,k)).
n a numeric value which represents the number of random vectors to be drawn (default is 1).

Description

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

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 (1998).

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, part 3.

See Also

Examples

x = linspace(-3,3,30)
pdf = dmsn([x',zeros(30,1)], [0,0], eye(2), [2,3])
#
rnd = rmsn(50,[0,0], eye(2),[2,3])


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