lawstat (version 3.2)

nig.parameter: Generating parameters for the normal inverse Gaussian (NIG) distribution

Description

The function produces 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.

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.

Details

The parameters are generated on three conditions: 1. $3*kurtosis > 5*skewness^2$, 2. $skewness > 0$, and 3. $variance > 0$.

References

Atkinson, A. C. (1982). The simulation of generalized inverse Gaussian and hyperbolic random variables. SIAM Journal on Scientific and Statistical Computing 3, 502-515.

Barndorff-Nielsen O., Blaesild, P. (1983). Hyperbolic distributions. In Encyclopedia of Statistical Sciences, Eds., Johnson N.L., Kotz S. and Read C.B., Vol. 3, pp. 700-707. New York: Wiley.

Noguchi, K. and Gel, Y. R. (2009) Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives. Working paper, Department of Statistics and Actuarial Science, University of Waterloo.

See Also

rnig (in fBasics package)

Examples

# NOT RUN {
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)
##   [1] 0.0003896483
var(random)
##   [1] 2.007351
kurtosis(random)
##   [1] 5.085051
##   attr(,"method")
##   [1] "excess"
skewness(random)
##   [1] 1.011352
##   attr(,"method")
##   [1] "moment"

# }