gig-distribution: The Generalized Inverse Gaussian Distribution

In ghyp: Generalized Hyperbolic Distribution and Its Special Cases

The Generalized Inverse Gaussian Distribution

Description

Density, distribution function, quantile function, random generation, expected shortfall and expected value and variance for the generalized inverse gaussian distribution.

Usage

dgig(x, lambda = 1, chi = 1, psi = 1, logvalue = FALSE)

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)

ESgig(alpha, lambda = 1, chi = 1, psi = 1, distr = c("return", "loss"), ...)

Egig(lambda, chi, psi, func = c("x", "logx", "1/x", "var"), check.pars = TRUE)

Arguments

x	A vector of quantiles.
q	A vector of quantiles.
p	A vector of probabilities.
alpha	A vector of confidence levels.
n	Number of observations.
lambda	A shape and scale and parameter.
chi, psi	Shape and scale parameters. Must be positive.
logvalue	If TRUE the logarithm of the density will be returned.
distr	Whether the ghyp-object specifies a return or a loss-distribution (see Details).
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 with the method “splines” instead of “integration”.
root.tol	The tolerance of uniroot.
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.

Details

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 relies on the C function with the same name kindly provided by Ester Pantaleo and Robert B. Gramacy.

Egig with func = "log x" uses grad from the R package numDeriv. See the package vignette for details regarding the expectation of GIG random variables.

Value

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.

Author(s)

David Luethi and Ester Pantaleo

References

Dagpunar, J.S. (1989). An easily implemented generalised inverse Gaussian generator. Commun. Statist. -Simula., 18, 703–710.

Michael, J. R, Schucany, W. R, Haas, R, W. (1976). Generating random variates using transformations with multiple roots, The American Statistican, 30, 88–90.

See Also

fit.ghypuv, fit.ghypmv, integrate, uniroot, spline

Examples

dgig(1:40, lambda = 10, chi = 1, psi = 1)
qgig(1e-5, lambda = 10, chi = 1, psi = 1)

ESgig(c(0.19,0.3), lambda = 10, chi = 1, psi = 1, distr = "loss")
ESgig(alpha=c(0.19,0.3), lambda = 10, chi = 1, psi = 1, distr = "ret")

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")

ghyp documentation built on Sept. 12, 2024, 7:38 a.m.