st.cumulants {sn} | R Documentation |
Cumulants of the skew-t distribution and inverse matching
st.cumulants(location = 0, scale = 1, shape = 0, df = Inf, n = 4) st.cumulants(dp=, n = 4) st.cumulants.inversion(cum, abstol = 1e-08)
location |
location parameter (vector) |
scale |
scale parameter (vector) |
shape |
shape parameter (vector) |
df |
degrees of freedom (scalar); default is df=Inf which corresponds
to the skew-normal distribution.
|
dp |
a vector of four elements, whose elements are (location, scale,
shape, df) respectively. If dp is specified, then
the individual parameters must not be.
|
n |
a scalar integer of the maximal order or cumulants required;
it must be from 1 to 4 and smaller than df
|
cum |
a vector of 4 elements which are taken to represent the first 4 cumulants of a skew-t distribution |
abstol |
a scalar which regulates the accuracy of the cumulants matching (default value 1e-08) |
Expressions of the moments and other details on the skew-t distribution are
given in the reference below. These formulae are used by st.cumulants
to compute the cumulants.
st.cumulants.inversion
searches the set of shape
and df
parameters of the skew-t family, attempting to match the third and fourth
cumulants with those of the supplied vector cum
.
This search is done numerically twice,
once using optim
and a second time using nlminb
,
to the accuracy abstol
; the best matching solution is retained.
If the required accuracy of the matching is not achieved by any of the
two methods, a warning message is issued.
After this step, the other two parameters (location
and
scale
) are computed via simple algebra.
st.cumulants
computes the cumulants up to order n
of
the skew-t distribution with the selected parameters. The returned object
is a vector of length n
if the parameters are all scalar,
otherwise a matrix with n
columns.
st.cumulants.inversion
returns a vector with the dp
parameters
of the matching skew-t distribution
The joint use st.cumulants.inversion
and
sample.centralmoments
allows to fit a skew-t distribution
by the methods of moments; see the example below
Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J.Roy. Statist. Soc. B 65, 367–389.
sn.cumulants
,dst
,
sample.centralmoments
, optim
,
nlminb
st.cumulants(shape=c(0,3,9), df=5) cum <- st.cumulants(dp=c(10, 2, -8, 5.2)) st.cumulants.inversion(cum) # data(ais, package='sn') mom <- sample.centralmoments(ais[,"bmi"]) st.cumulants.inversion(cum=c(mom[1:3],mom[4]-3*mom[2]^2)) # parameters of the fitted ST distribution