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

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## 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

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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)

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