| 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,length(alpha)), Omega, alpha, log=FALSE) dmsn(x, dp=, log=FALSE) pmsn(x, xi=rep(0,length(alpha)), Omega, alpha, ...) pmsn(x, dp=) rmsn(n=1, xi=rep(0,length(alpha)), Omega, alpha) rmsn(n=1, dp=)
x |
for dmsn, this is either a vector of length d,
where d=length(alpha), or a matrix with d columns,
giving the coordinates of the point(s) where the density must
be evaluated;
for pmsn, only a vector of length d is allowed.
|
xi |
a numeric vector of length 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.
|
Omega |
a positive-definite covariance matrix of dimension (d,d).
|
alpha |
a numeric vector which regulates the shape of the density. |
dp |
a list with three elements named xi, Omega and alpha
containing quantities as described above. If dp is specified, this
overrides the individual parameter specification.
|
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 pmnorm
|
The positive-definiteness of Omega is not tested for
efficiency reasons. Function pmsn requires pmnorm
from package mnormt;
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,-6) pdf <- dmsn(cbind(x,2*x-1), xi, Omega, alpha) rnd <- rmsn(10, xi, Omega, alpha) p1 <- pmsn(c(2,1), xi, Omega, alpha) p2 <- pmsn(c(2,1), xi, Omega, alpha, abseps=1e-12, maxpts=10000)