nig.parameter {lawstat}R Documentation

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.

Details

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

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, 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


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"


[Package lawstat version 2.3 Index]