sn (version 2.1.1)

modeSECdistr: The mode of a skew-elliptically contoured (SEC) distribution

Description

Compute compute the mode of a univariate or multivariate SEC distribution.

Usage

modeSECdistr(dp, family, object=NULL)

Value

a numeric vector

Arguments

dp

a numeric vector (in the univariate case, for class SECdistrUv) or a list (in the multivariate case, , for class SECdistrUv) of parameters which identify the specific distribution within the named family.

family

a character string which identifies the parametric family among those admissible for classes SECdistrUv or SECdistrMv.

object

an object of class SECdistrUv or SECdistrMv as created by makeSECdistr or extractSECdistr; if this argument is used, arguments dp and family must not be set, and vice versa.

Background

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.

References

Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.

See Also

makeSECdistr and extractSECdistr for additional information and for constructing a suitable object,

SECdistrUv-class and SECdistrMv-class for methods mean and vcov which compute the mean (vector) and the variance (matrix) of the object distribution

Examples

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"))
mode1 <- modeSECdistr(dp3, "ST")
mode2 <- modeSECdistr(object=st3) # the same of mode1