modeSECdistr {sn}

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)

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.

Value

a numeric vector

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