nig.parameter {lawstat}

Generate Parameters for the Normal Inverse Gaussian (NIG) Distribution

Description

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

Usage

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

Arguments

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.

Details

The parameters are generated with three conditions: 1) 3\times kurtosis > 5\times skewness^2; 2) skewness > 0, and 3) variance > 0. See Atkinson (1982), Barndorff-Nielsen and Blaesild (1983), and Noguchi and Gel (2010).

Value

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.

Author(s)

Kimihiro Noguchi, Yulia R. Gel

References

Atkinson AC (1982). “The simulation of generalized inverse Gaussian and hyperbolic random variables.” SIAM Journal on Scientific and Statistical Computing, 3(4), 502–515. doi:10.1137/0903033.

Barndorff-Nielsen OE, Blaesild P (1983). “Hyperbolic distributions.” In Johnson NL, Kotz S, Read CB (eds.), Encyclopedia of Statistical Sciences, 700–707. John Wiley & Sons Ltd, New York.

Noguchi K, Gel YR (2010). “Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives.” Journal of Nonparametric Statistics, 22(7), 897–913. doi:10.1080/10485251003698505.

See Also

rnig

Examples

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)