ghyp-constructors {ghyp} | R Documentation |
Constructor function for univariate and multivariate generalized hyperbolic objects and its special cases.
ghyp(lambda = 0.5, chi = 0.5, psi = 2, mu = 0, sigma = 1, gamma = 0, alpha.bar = NULL, data = NULL) hyp(chi = 0.5, psi = 2, mu = 0, sigma = 1, gamma = 0, alpha.bar = NULL, data = NULL) NIG(chi = 2, psi = 2, mu = 0, sigma = 1, gamma = 0, alpha.bar = NULL, data = NULL) student.t(nu = 3.5, mu = 0, sigma = 1, gamma = 0, data = NULL) VG(lambda = 1, psi = 2*lambda, mu = 0, sigma = 1, gamma = 0, data = NULL)
lambda |
Shape parameter. |
nu |
Shape parameter only used in case of a student-t distribution. It determines the degree of freedom. |
chi |
Shape parameter of the alternative “chi/psi” parametrization. |
psi |
Shape parameter of the alternative “chi/psi” parametrization. |
alpha.bar |
Shape parameter of the alternative “alpha.bar” parametrization. Supplying “alpha.bar” makes the parameters “chi” and “psi” redundant. |
mu |
Location parameter. Either a scalar or a vector. |
sigma |
Dispersion parameter. Either a scalar or a matrix. |
gamma |
Skewness parameter. Either a scalar or a vector. |
data |
An object coercible to a vector (univariate case)
or matrix (multivariate case). |
This function serves as a constructor for univariate and multivariate
generalized hyperbolic distribution objects and the special cases of the
generalized hyperbolic distribution.
ghyp
, hyp
and NIG
can be called either with the
“chi/psi” or the “alpha.bar” parametrization.
When ever alpha.bar
is not NULL
it is assumed that the “alpha.bar”
parametrization is used and the parameters “chi” and “psi” become redundant.
An object of class ghyp
.
The Student-t parametrization obtained via the “alpha.bar” parametrization slightly differs
from the common student-t parametrization: The parameter sigma
denotes the standard
deviation in the univariate case and the variance in the multivariate case.
Thus, set sigma = sqrt(nu /(nu-2)
in the univariate case to get the same results as
with the standard R implementation of the student-t distribution.
Have a look on the vignette of this package in the doc
folder.
Once an object of class ghyp
is created the methods
Xghyp
have to be used even when the distribution is a special case of
the generalized hyperbolic distribution. E.g. do not use dVG
.
Use dghyp
and submit a variance gamma
distribution created with VG()
.
David Lüthi
ghyp-class
for a summary of generic methods belonging to ghyp
objects,
fit.ghypuv
and fit.ghypmv
for fitting routines.
## alpha.bar parametrization of a univariate generalized hyperbolic distribution ghyp(lambda=1, alpha.bar=0.1, mu=0, sigma=1, gamma=0) ## lambda/chi parametrization of a univariate generalized hyperbolic distribution ghyp(lambda=1, chi=1, psi=0.5, mu=0, sigma=1, gamma=0) ## alpha.bar parametrization of a multivariate generalized hyperbolic distribution ghyp(lambda=1, alpha.bar=0.1, mu=rep(0,2), sigma=diag(rep(1,2)), gamma=rep(0,2)) ## lambda/chi parametrization of a multivariate generalized hyperbolic distribution ghyp(lambda=1, chi=1, psi=0.5, mu=rep(0,2), sigma=diag(rep(1,2)), gamma=rep(0,2)) ## alpha.bar parametrization of a univariate hyperbolic distribution hyp(alpha.bar=0.3, mu=1, sigma=0.1, gamma=0) ## lambda/chi parametrization of a univariate hyperbolic distribution hyp(chi=1, psi=2, mu=1, sigma=0.1, gamma=0) ## alpha.bar parametrization of a univariate normal inverse gaussian distribution NIG(alpha.bar=0.3, mu=1, sigma=0.1, gamma=0) ## lambda/chi parametrization of a univariate normal inverse gaussian distribution NIG(chi=1, psi=2, mu=1, sigma=0.1, gamma=0) ## alpha.bar parametrization of a univariate variance gamma distribution VG(lambda=2, mu=1, sigma=0.1, gamma=0) ## alpha.bar parametrization of a univariate student-t distribution student.t(nu = 3, mu=1, sigma=0.1, gamma=0)