gig-distribution: The Generalized Inverse Gaussian Distribution
In ghyp: A package on the generalized hyperbolic distribution and its special cases

Description Usage Arguments Details Value Author(s) References See Also Examples

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, 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)

`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`.

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.

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 Luethi and Ester Pantaleo

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.

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

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")

Loading required package: numDeriv
Loading required package: gplots

Attaching package: 'gplots'

The following object is masked from 'package:stats':

    lowess

 [1] 1.017854e-09 4.058652e-07 1.028601e-05 8.662516e-05 4.013694e-04
 [6] 1.277222e-03 3.139139e-03 6.389523e-03 1.126445e-02 1.773343e-02
[11] 2.547732e-02 3.394288e-02 4.244752e-02 5.029911e-02 5.690051e-02
[16] 6.182046e-02 6.482518e-02 6.587466e-02 6.509325e-02 6.272601e-02
[21] 5.909098e-02 5.453489e-02 4.939724e-02 4.398448e-02 3.855432e-02
[26] 3.330887e-02 2.839460e-02 2.390695e-02 1.989775e-02 1.638384e-02
[31] 1.335568e-02 1.078530e-02 8.633089e-03 6.853261e-03 5.398022e-03
[36] 4.220558e-03 3.277017e-03 2.527684e-03 1.937542e-03 1.476391e-03
[1] 3.383629
[1] 21.95485 22.98326
[1] 11.95756 13.22362
[1] 20.05536
[1] 40.00038
[1] 0.05536417