dmsn {sn} | R Documentation |
Probability density function and random number generation for the multivariate skew-normal (MSN) distribution.
dmsn(x, xi=rep(0,k), Omega, alpha) rmsn(n=1, xi=rep(0,k), Omega, alpha)
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 .
|
n |
a numeric value which represents the number of random vectors to be drawn. |
A vector of density values (dmsn
), or a matrix of random
points (rmsn
).
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).
Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715726.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579602.
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))