Generalized Inverse Gaussian {ghyp} | R Documentation |
Density, distribution function, quantile function, random generation, expected shortfall and expected value and variance for the generalized inverse gaussian distribution.
dgig(x, lambda = 1, chi = 1, psi = 1) pgig(q, lambda = 1, chi = 1, psi = 1, ...) qgig(p, lambda = 1, chi = 1, psi = 1, method = c("integration", "splines"), spline.points = 200, subdivisions = 200, root.tol = .Machine$double.eps^0.5, rel.tol = root.tol^1.5, abs.tol = rel.tol, ...) rgig(n = 10, lambda = 1, chi = 1, psi = 1, envplot = F, messages = F) ESgig(p, lambda = 1, chi = 1, psi = 1, ...) Egig(lambda, chi, psi, func = c("x", "logx", "1/x", "var"), check.pars = T)
x |
A vector of quantiles. |
q |
A vector of quantiles. |
p |
A vector of probabilities. |
n |
Number of observations. |
lambda |
A shape and scale and parameter. |
chi, psi |
Shape and scale parameters. Must be positive. |
subdivisions |
The number of subdivisions passed to integrate when computing
the the distribution function pgig . |
rel.tol |
The relative accuracy requested from integrate . |
abs.tol |
The absolute accuracy requested from integrate . |
method |
Determines which method is used when calculating quantiles. |
spline.points |
The number of support points when computing the quantiles using
splines instead of integration. |
root.tol |
The tolerance of uniroot . |
messages |
If TRUE error messages from rgig are printed. |
envplot |
If TRUE an plot of the envelope is shown. |
func |
The transformation function when computing the expected value.
x is the expected value (default), log x returns the
expected value of the logarithm of x , 1/x returns the
expected value of the inverse of x and var returns the
variance. |
check.pars |
If TRUE the parameters are checked first. |
... |
Arguments passed form ESgig to qgig . |
qgig
computes the quantiles either by using the “integration” method where the root of
the distribution function is solved or via “splines” which interpolates the distribution
function and solves it with uniroot
afterwards. The “integration”
method is recommended when few quantiles are required. If more than approximately
20 quantiles are needed to be calculated the “splines” method becomes faster.
The accuracy can be controlled with an adequate setting of the
parameters rel.tol
, abs.tol
, root.tol
and spline.points
.
rgig
uses the random generator from the S-Plus library QRMlib
(see http://www.math.ethz.ch/~mcneil/book/QRMlib.html).
dgig
gives the density,
pgig
gives the distribution function,
qgig
gives the quantile function,
ESgig
gives the expected shortfall,
rgig
generates random deviates and
Egig
gives the expected value
of either x
, 1/x
, log(x)
or the variance if func
equals var
.
David Lüthi
The algorithm for simulating generalized inverse gaussian variates is copied from the S-Plus and R library QRMlib from Alexander J. McNeil (2005) designed to accompany the book Quantitative Risk Management, Concepts, Techniques and Tools. http://www.math.ethz.ch/~mcneil/book/QRMlib.html.
fit.ghypuv
, fit.ghypmv
, integrate
,
uniroot
dgig(1:40,lambda=10,chi=1,psi=1) qgig(1e-5,lambda=10,chi=1,psi=1) Egig(lambda=10,chi=1,psi=1,func="x") Egig(lambda=10,chi=1,psi=1,func="var") Egig(lambda=10,chi=1,psi=1,func="1/x")