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

modeSECdistr {sn} | R Documentation

## 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.`

### 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"))
    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")

[Package sn version 1.5-0 Index]