lawstat (version 3.4)

nig.parameter: 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
)

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.

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.

Author

Kimihiro Noguchi, Yulia R. Gel

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;textuallawstat, BarndorffNielsen_Blaesild_1983;textuallawstat, and Noguchi_Gel_2010;textuallawstat.

References

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)