summary.SECdistr: Summary of a SEC distribution object
In sn: The Skew-Normal and Related Distributions Such as the Skew-t and the SUN
summary.SECdistr 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.
Details
For a description of the DP, CP and
pseudo-CP parameter sets included in the returned object,
see dp2cp.
The aux slot of the returned object includes other summary quantities,
as described next.
In the univariate case, the reported quantile-based measures of skewness and
kurtosis refer to the Bowley and Moors measures, respectively;
see Groeneveld (2006) and Moors (1988) for their specifications.
In the multivariate case, the Mardia's measures of skewness and kurtosis
are computed from the expressions given on p.153 and p.178 of
Azzalini and Capitanio (2014).
In the univariate case, delta is a simple transformation of the
slant parameter alpha; it takes values in (-1, 1).
In the multivariate case, delta is a vector with components
of similar type; they correspond to the matching terms of the univariate
components. The alpha* and delta* coefficients are univariate
comprehensive summary quantities of slant; see pp.132-3 of
Azzalini and Capitanio (2014) for their expressions. These quantities
play an important role in SEC distributions; for instance,
the Mardia's measures of multivariare skewness and kurtosis depend
on the vector of slant parameters only via delta* or, equivalently,
via alpha*.
The mode, which is unique for all these distributions, is computed by a
numerical line search between the DP location and the CP
location (or the pseudo-DP location, when the latter does
exists). This line search is univariate also in the multivariate case,
using Propositions 5.14 and 6.2 of Azzalini and Capitanio (2014);
see also Problem 5.14.
The examples below illustrate how extract various components from aux
and other slots of the returned object.
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); see Section ‘Details’ for more information.
The list items dp and cp are vectors if class(object) is
SECdistrUv (univariate distribution); they are lists if
class(object) is SECdistrMv (multivariate distribution).
Author(s)
Adelchi Azzalini
References
Azzalini, A. with the collaboration of Capitanio, A. (2014).
The Skew-Normal and Related Families.
Cambridge University Press, IMS Monographs series.
Moors, I. J. A. (1988). A quantile alternative for kurtosis.
The Statistician 37, 25-32.
Groeneveld, R. A. (2006). Skewness, Bowley's measures of.
In volume 12, 7771-3, of Encyclopedia of Statistical Sciences,
2nd edition, edited by Kotz et al. Wiley, New York.
See Also
makeSECdistr for building a SEC distribution
extractSECdistr for extracting a SEC
distribution from a selm fit
methods mean and sd
for computing the mean and the standard deviation of
SECdistrUv-class objects,
methods mean and vcov
for computing the mean vector and the variance matrix of
SECdistrMv-class objects
modeSECdistr for computing the mode directly
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", name="ST3", 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 skewness 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)
sn documentation built on April 5, 2023, 5:15 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| summary.SECdistr | 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 |
cp.type |
a character string to select the required variance of
CP parameterization; possible values are |
probs |
in the univariate case, a vector of probabilities for which
the corresponding quantiles are required. If missing, the vector
|
Details
For a description of the DP, CP and
pseudo-CP parameter sets included in the returned object,
see dp2cp.
The aux slot of the returned object includes other summary quantities,
as described next.
In the univariate case, the reported quantile-based measures of skewness and
kurtosis refer to the Bowley and Moors measures, respectively;
see Groeneveld (2006) and Moors (1988) for their specifications.
In the multivariate case, the Mardia's measures of skewness and kurtosis
are computed from the expressions given on p.153 and p.178 of
Azzalini and Capitanio (2014).
In the univariate case, delta is a simple transformation of the
slant parameter alpha; it takes values in (-1, 1).
In the multivariate case, delta is a vector with components
of similar type; they correspond to the matching terms of the univariate
components. The alpha* and delta* coefficients are univariate
comprehensive summary quantities of slant; see pp.132-3 of
Azzalini and Capitanio (2014) for their expressions. These quantities
play an important role in SEC distributions; for instance,
the Mardia's measures of multivariare skewness and kurtosis depend
on the vector of slant parameters only via delta* or, equivalently,
via alpha*.
The mode, which is unique for all these distributions, is computed by a numerical line search between the DP location and the CP location (or the pseudo-DP location, when the latter does exists). This line search is univariate also in the multivariate case, using Propositions 5.14 and 6.2 of Azzalini and Capitanio (2014); see also Problem 5.14.
The examples below illustrate how extract various components from aux
and other slots of the returned object.
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); see Section ‘Details’ for more information. |
The list items dp and cp are vectors if class(object) is
SECdistrUv (univariate distribution); they are lists if
class(object) is SECdistrMv (multivariate distribution).
Author(s)
Adelchi Azzalini
References
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
Moors, I. J. A. (1988). A quantile alternative for kurtosis. The Statistician 37, 25-32.
Groeneveld, R. A. (2006). Skewness, Bowley's measures of. In volume 12, 7771-3, of Encyclopedia of Statistical Sciences, 2nd edition, edited by Kotz et al. Wiley, New York.
See Also
makeSECdistr for building a SEC distribution
extractSECdistr for extracting a SEC
distribution from a selm fit
methods mean and sd
for computing the mean and the standard deviation of
SECdistrUv-class objects,
methods mean and vcov
for computing the mean vector and the variance matrix of
SECdistrMv-class objects
modeSECdistr for computing the mode directly
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")$q.measures # quantile-based measures of skewness and kurtosis
#
dp3 <- list(xi=1:3, Omega=toeplitz(1/(1:3)), alpha=c(-3, 8, 5), nu=6)
st3 <- makeSECdistr(dp=dp3, family="ST", name="ST3", compNames=c("U", "V", "W"))
s <- summary(st3)
dp <- slot(s, "dp") # the same of slot(st3, "dp")
slot(s, "cp")$var.cov # the same of vcov(st3)
slot(s, "aux")$delta.star # comprehensive coefficient of shape
slot(s, "aux")$mardia # Mardia's measures of skewness 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)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.