nig.parameter: Generate Parameters for the Normal Inverse Gaussian (NIG)...

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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 \insertCiteAtkinson_1982;textuallawstat, \insertCiteBarndorffNielsen_Blaesild_1983;textuallawstat, and \insertCiteNoguchi_Gel_2010;textuallawstat.

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

\insertAllCited

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)

lawstat documentation built on April 6, 2023, 1:06 a.m.