dmsn {sn} | R Documentation |
Probability density function, distribution function and random number generation for the multivariate skew-normal (MSN) distribution.
dmsn(x, xi=rep(0,d), Omega, alpha, log=FALSE) pmsn(x, xi=rep(0,d), Omega, alpha, ...) rmsn(n=1, xi=rep(0,d), Omega, alpha)
x |
for dmsn , this is either a vector of length d or a matrix
with d columns (where d=length(alpha) ), giving
the coordinates of the point(s) where the density must be avaluated;
for pmsn , only a vector of length d is allowed.
|
Omega |
a positive-definite covariance matrix of dimension (d,d) .
|
alpha |
a numeric vector which regulates the shape of the density. |
xi |
a numeric vector of lenght d , or a matrix with d 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. |
log |
logical; if TRUE, densities are given as log-densities. |
... |
additional parameters passed to pmvnorm
|
The positive-definiteness of Omega
is not tested for
efficiency reasons. Function
pmsn
requires pmvnorm
from library(mvtnorm)
;
the accuracy of its computation can be controlled via use of ...
A vector of density values (dmsn
), or a single probability
(pmsn
) 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, 715–726.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579–602.
x <- seq(-3,3,length=15) xi <- c(0.5, -1) Omega <- diag(2) Omega[2,1] <- Omega[1,2] <- 0.5 alpha <- c(2,2) pdf <- dmsn(cbind(x,2*x-1), xi, Omega, alpha) rnd <- rmsn(10, xi, Omega, alpha) library(mvtnorm) # only once in the session cdf <- pmsn(c(2,1), xi, Omega, alpha)