msn.affine {sn} | R Documentation |
Computes the parameters of an affine transformation a+ A Y of a multivariate skew-normal or skew-t variable Y
msn.affine(dp, A, a=0, drop=TRUE) mst.affine(dp, A, a=0, drop=TRUE)
dp |
a list containg the pamaters of the variable being
transformed; it must include components xi , Omega ,
alpha as described for dmsn ; for mst.affine ,
also a component df is expected
|
A |
a matrix with ncol(A) equal to nrow(dp$Omega)
|
a |
a vector wiht length(a) equal to nrow(dp$Omega)
|
drop |
a logical flag (default value is TRUE ) operating when
nrow(A) equals 1. If these conditions are met, the output
is provided in the form of parameters of a scalar distribution,
dsn or dst , depending in the case.
|
A list containing the same components of the input parameter dp
For background information about the skew-normal and skew-t distributions, their parameters and the properties of affine transformations, see the references below.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579602.
Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J.Roy. Statist. Soc. B 65, 367389.
Capitanio, A. et al. (2003). Graphical models for skew-normal variates. Scand. J. Statist. 30, 129144.
dp<- list(xi=c(1,1,2), Omega=toeplitz(1/1:3), alpha=c(3,-1,2)) A <- matrix(c(1,-1,1,3,0,-2), 2, 3, byrow=TRUE) dp1 <- msn.affine(dp, A, 1:2) # dp$df <- 5 dp2<- mst.affine(dp,A[1,,drop=FALSE]) dp3<- mst.affine(dp,A[1,,drop=FALSE], drop=FALSE) if(zapsmall(dp2$scale^2 - dp3$Omega)) print("something wrong here!")