R: Summary of a SEC distribution object

summary.SECdistr {sn} | R Documentation

## Summary of a SEC distribution object

### Description

Produce a summary of an object of class either `"SECdistrUv"` or `"SECdistrMv"`, which refer to a univariate or a multivariate SEC distribution, respectively. Both types of objects can be produced by `makeSECditr`.

### Usage

    ## S4 method for signature 'SECdistrUv'
    summary(object, cp.type = "auto", probs)

    ## S4 method for signature 'SECdistrMv'
    summary(object, cp.type = "auto")

### Arguments

`object` | an object of class `"SECdistrUv"` or `"SECdistrMv"`.
`cp.type` | a character string to select the required variance of CP parameterization; possible values are `"proper"`, `"pseudo"`, `"auto"` (default). For a description of these codes, see `dp2cp`.
`probs` | in the univariate case, a vector of probabilities for which the corresponding quantiles are required. If missing, the vector `c(0.05, 0.25, 0.50, 0.75, 0.95)` is used.

### Value

A list with the following components:

`family` | name of the family within the SEC class, character
`dp` | DP parameters, a list or a vector
`name` | the name of the distribution, character string
`compNames` | in the multivariate case the names of the components, a character vector
`cp` | CP parameters, a list or a vector
`cp.type` | the name of the selected variant of the CP set
`aux` | a list with auxiliary ingredients (mode, coefficients of skewness and kurtosis, in the parametric and non-parametric variants, and more).

DP and CP are vectors if `class(object)` is `SECdistrUv` (univariate distribution); they are lists if codeclass(object) is `SECdistrMv` (multivariate distribution). The examples below show how extract components from `aux` and other slots.

### Author(s)

Adelchi Azzalini

### See Also

`makeSECdistr` for extracting a SEC distribution from a `selm` fit

methods `mean` and `vcov` for computing the mean (vector) and the variance (matrix) of `SECdistrUv-class` and `SECdistrMv-class` objects

### Examples

    f3 <- makeSECdistr(dp=c(3,2,5), family="SC")
    summary(f3)
    s <- summary(f3, probs=(1:9)/10)
    print(slotNames(s))
    print(names(slot(s,"aux")))   # the components of the 'aux' slot
    slot(s, "aux")$mode           # the same of modeSECdistr(object=f3)
    slot(s, "aux")$q.measures     # quantile-based measures of skewness and kurtosis
    #
    dp3 <- list(xi=1:3, Omega=toeplitz(1/(1:3)), alpha=c(-3, 8, 5), nu=6)
    st3 <- makeSECdistr(dp=dp3, family="ST", compNames=c("U", "V", "W"))
    s <- summary(st3)
    dp <- slot(s, "dp")           # the same of slot(st3, "dp")
    slot(s, "cp")$var.cov         # the same of vcov(st3)
    slot(s, "aux")$delta.star     # comprehensive coefficient of shape
    slot(s, "aux")$mardia         # Mardia's measures of asymmetry and kurtosis
    #
    dp2 <- list(xi=rep(0,2), Omega=matrix(c(2,2,2,4),2,2), alpha=c(3,-5), tau=-1)
    esn2 <- makeSECdistr(dp=dp2, family="ESN", name="ESN-2d")
    summary(esn2)

[Package sn version 1.5-0 Index]