PoweR (version 1.0.7)

law0037.NormalInvGaussian: 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 $\delta {\alpha }^2/{\gamma }^3$.

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

# NOT RUN {
res <- gensample(37,10000,law.pars=c(3,2,1,0.5))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }