The mode of a skew-elliptically contoured (SEC) distribution
Compute compute the mode of a univariate or multivariate SEC distribution.
a numeric vector (in the univariate case, for class
a character string which identifies the parametric
family among those admissible for classes
an object of class
a numeric vector
The mode is obtained through numerical maximization. In the multivariate case, the problem is reduced to a one-dimensional search using Propositions 5.14 and 6.2 of the reference below.
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
for additional information and for constructing a suitable
vcov which compute the mean (vector)
and the variance (matrix) of the
1 2 3 4 5 6
dp3 <- list(xi=1:3, Omega=toeplitz(1/(1:3)), alpha=c(3,-1,2), nu=5) st3 <- makeSECdistr(dp3, family="ST", name="ST3", compNames=c("U", "V", "W")) A <- matrix(c(1,-1,1, 3,0,-2), 3, 2) new.st <- affineTransSECdistr(st3, a=c(-3,0), A=A) # st2 <- marginalSECdistr(st3, comp=c(3,1), name="2D marginal of ST3")