law0037.NormalInvGaussian {PoweR} | R Documentation |
The Normal-inverse Gaussian Distribution
Description
Random generation for the Normal-inverse Gaussian distribution with parameters shape
, skewness
, location
and scale
.
This generator is called by function gensample
to create random variables based on its parameters.
Details
If shape
, skewness
, location
and scale
are not specified they assume the default values of 1, 0, 0 and 1, respectively.
The Normal-inverse Gaussian distribution with parameters shape =
\alpha
,
skewness =
\beta
, location =
\mu
and scale =
\delta
has density:
\frac{\alpha\delta K_1(\alpha\sqrt{\delta^2+(x-\mu)^2})}{\pi\sqrt{\delta^2+(x-\mu)^2}}e^{\delta\gamma+\beta(x-\mu)}
where \gamma = \sqrt(\alpha^2 - \beta^2)
and
K_1
denotes a modified Bessel function of the second kind.
The mean and variance of NIG are defined respectively \mu + \beta \delta / \gamma
and
\delta \alpha^2 / \gamma^3
.
Author(s)
P. Lafaye de Micheaux, V. A. Tran
References
Pierre Lafaye de Micheaux, Viet Anh Tran (2016). PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Studies for Goodness-of-fit Tests in R. Journal of Statistical Software, 69(3), 1–42. doi:10.18637/jss.v069.i03
See Also
See package fBasics
. See Distributions
for other standard distributions.
Examples
res <- gensample(37,10000,law.pars=c(3,2,1,0.5))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)