nig.parameter: Generate Parameters for the Normal Inverse Gaussian (NIG)...
In gel-research-group/lawstat: Tools for Biostatistics, Public Policy, and Law

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

Produce four parameters, alpha (tail heavyness), beta (asymmetry), delta (scale), and mu (location) from the four variables: mean, variance, kurtosis, and skewness.

nig.parameter(
  mean = mean,
  variance = variance,
  kurtosis = kurtosis,
  skewness = skewness
)

`mean`	mean of the NIG distribution.
`variance`	variance of the NIG distribution.
`kurtosis`	excess kurtosis of the NIG distribution.
`skewness`	skewness of the NIG distribution.

The parameters are generated with three conditions: 1) 3\times kurtosis > 5\times skewness^2; 2) skewness > 0, and 3) variance > 0. See \insertCiteAtkinson_1982;textuallawstat, \insertCiteBarndorffNielsen_Blaesild_1983;textuallawstat, and \insertCiteNoguchi_Gel_2010;textuallawstat.

A list with the following numeric components:

`alpha`	tail-heavyness parameter of the NIG distribution.
`beta`	asymmetry parameter of the NIG distribution.
`delta`	scale parameter of the NIG distribution.
`mu`	location parameter of the NIG distribution.

Kimihiro Noguchi, Yulia R. Gel

\insertAllCited

rnig

library(fBasics)
test <- nig.parameter(0, 2, 5, 1)
random <- rnig(1000000, alpha = test$alpha, beta = test$beta, 
               mu = test$mu, delta = test$delta)
mean(random)
var(random)
kurtosis(random)
skewness(random)