ghyp-constructors {ghyp} | R Documentation |
Constructor functions for univariate and multivariate generalized hyperbolic distribution objects and their special cases in one of the parametrizations “chi/psi”, “alpha.bar” and “alpha/delta”.
ghyp(lambda = 0.5, chi = 0.5, psi = 2, mu = 0, sigma = diag(rep(1, length(mu))), gamma = rep(0, length(mu)), alpha.bar = NULL, data = NULL) ghyp.ad(lambda = 0.5, alpha = 1.5, delta = 1, beta = rep(0, length(mu)), mu = 0, Delta = diag(rep(1, length(mu))), data = NULL) hyp(chi = 0.5, psi = 2, mu = 0, sigma = diag(rep(1, length(mu))), gamma = rep(0, length(mu)), alpha.bar = NULL, data = NULL) hyp.ad(alpha = 1.5, delta = 1, beta = rep(0, length(mu)), mu = 0, Delta = diag(rep(1, length(mu))), data = NULL) NIG(chi = 2, psi = 2, mu = 0, sigma = diag(rep(1, length(mu))), gamma = rep(0, length(mu)), alpha.bar = NULL, data = NULL) NIG.ad(alpha = 1.5, delta = 1, beta = rep(0, length(mu)), mu = 0, Delta = diag(rep(1, length(mu))), data = NULL) student.t(nu = 3.5, mu = 0, sigma = diag(rep(1, length(mu))), gamma = rep(0, length(mu)), data = NULL) student.t.ad(lambda = -2, delta = 1, beta = rep(0, length(mu)), mu = 0, Delta = diag(rep(1, length(mu))), data = NULL) VG(lambda = 1, psi = 2*lambda, mu = 0, sigma = diag(rep(1, length(mu))), gamma = rep(0, length(mu)), data = NULL) VG.ad(lambda = 2, alpha = 1.5, beta = rep(0, length(mu)), mu = 0, Delta = diag(rep(1, length(mu))), data = NULL) gauss(mu = 0, sigma = diag(rep(1, length(mu))), data = NULL)
lambda |
Shape parameter. Common for all parametrizations. |
nu |
Shape parameter only used in case of a Student-t distribution in the “chi/psi” and “alpha.bar” parametrization . It determines the degree of freedom. |
chi |
Shape parameter of the “chi/psi” parametrization. |
psi |
Shape parameter of the “chi/psi” parametrization. |
alpha |
Shape parameter of the “alpha/delta” parametrization. |
delta |
Shape parameter of the “alpha/delta” parametrization. |
alpha.bar |
Shape parameter of the “alpha.bar” parametrization. Supplying “alpha.bar” makes the parameters “chi” and “psi” redundant. |
mu |
Location parameter. Either a scalar or a vector. Common for all parametrizations. |
sigma |
Dispersion parameter of the “chi/psi” parametrization. Either a scalar or a matrix. |
Delta |
Dispersion parameter. Must be a matrix with a determinant of 1. This parameter is only used in the multivariate case of the “alpha.beta” parametrization. |
gamma |
Skewness parameter of the “chi/psi” parametrization. Either a scalar or a vector. |
beta |
Skewness parameter of the “alpha/delta” parametrization. Either a scalar or a vector. |
data |
An object coercible to a vector (univariate case)
or matrix (multivariate case). |
These functions serve as constructors 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. Whenever
alpha.bar
is not NULL
it is assumed that the
“alpha.bar” parametrization is used and the parameters
“chi” and “psi” become redundant.
ghyp.ad
, hyp.ad
, NIG.ad
, student.t.ad
and
VG.ad
use the “alpha/delta” parametrization. Have a
look on the vignette of this package in the doc
folder for
further information regarding the parametrization and for the domains
of variation of the parameters.
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 (see
Examples). Have a look on the vignette of this package in the
doc
folder for further information.
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 Luethi
ghyp
-package vignette in the doc
folder or on http://cran.r-project.org/web/packages/ghyp/
ghyp-class
for a summary of generic methods assigned to ghyp
objects,
coef
for switching between different parametrizations,
d/p/q/r/ES/gyhp
for density, distribution function et cetera,
fit.ghypuv
and fit.ghypmv
for fitting routines.
## alpha.bar parametrization of a univariate generalized hyperbolic distribution ghyp(lambda=2, alpha.bar=0.1, mu=0, sigma=1, gamma=0) ## lambda/chi parametrization of a univariate generalized hyperbolic distribution ghyp(lambda=2, chi=1, psi=0.5, mu=0, sigma=1, gamma=0) ## alpha/delta parametrization of a univariate generalized hyperbolic distribution ghyp.ad(lambda=2, alpha=0.5, delta=1, mu=0, beta=0) ## alpha.bar parametrization of a multivariate generalized hyperbolic distribution ghyp(lambda=1, alpha.bar=0.1, mu=2:3, sigma=diag(1:2), gamma=0:1) ## lambda/chi parametrization of a multivariate generalized hyperbolic distribution ghyp(lambda=1, chi=1, psi=0.5, mu=2:3, sigma=diag(1:2), gamma=0:1) ## alpha/delta parametrization of a multivariate generalized hyperbolic distribution ghyp.ad(lambda=1, alpha=2.5, delta=1, mu=2:3, Delta=diag(c(1,1)), beta=0:1) ## 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/delta parametrization of a univariate hyperbolic distribution hyp.ad(alpha=0.5, delta=1, mu=0, beta=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/delta parametrization of a univariate normal inverse gaussian distribution NIG.ad(alpha=0.5, delta=1, mu=0, beta=0) ## alpha.bar parametrization of a univariate variance gamma distribution VG(lambda=2, mu=1, sigma=0.1, gamma=0) ## alpha/delta parametrization of a univariate variance gamma distribution VG.ad(lambda=2, alpha=0.5, mu=0, beta=0) ## alpha.bar parametrization of a univariate Student-t distribution student.t(nu = 3, mu=1, sigma=0.1, gamma=0) ## alpha/delta parametrization of a univariate Student-t distribution student.t.ad(lambda=-2, delta=1, mu=0, beta=1) ## Obtain equal results as in the R-core parametrization of the Student-t distribution nu <- 2.1 t.obj <- student.t(nu = nu, sigma = sqrt(nu / (nu - 2))) dat <- 0.1 * 1:9 dt(dat, nu) dghyp(dat, t.obj) pt(dat, nu) pghyp(dat, t.obj)