dmsn {sn} | R Documentation |
Probability density function, distribution function and random number generation for the multivariate skew-normal (SN) distribution.
dmsn(x, xi=rep(0,length(alpha)), Omega, alpha, tau=0, dp=NULL, log=FALSE) pmsn(x, xi=rep(0,length(alpha)), Omega, alpha, tau=0, dp=NULL, ...) rmsn(n=1, xi=rep(0,length(alpha)), Omega, alpha, tau=0, dp=NULL)
x |
for |
xi |
a numeric vector of length |
Omega |
a symmetric positive-definite matrix of dimension |
alpha |
a numeric vector which regulates the slant of the density;
see ‘Background’. |
tau |
a single value representing the ‘hidden mean’ parameter
of the ESN distribution; |
dp |
a list with three elements, corresponding to |
n |
a numeric value which represents the number of random vectors to be drawn. |
log |
logical (default value: |
... |
additional parameters passed to |
Typical usages are
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=)
Function pmsn
makes use of pmnorm
from package mnormt;
the accuracy of its computation can be controlled via ...
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).
Chapter 5 of Azzalini and Capitanio (2014) provides an extensive account,
including subsequent developments.
Notice that the location vector xi
does not represent the mean vector
of the distribution. Similarly, Omega
is not the covariance
matrix of the distribution, although it is a covariance matrix.
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. Full-length version available at http://arXiv.org/abs/0911.2093
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
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)