nig.parameter {lawstat} | R Documentation |
The function produces four parameters, alpha (tail heavyness), beta (asymmetry), delta (scale), and mu (location) from the four variables, mean, variance, kurtosis, and skewness.
nig.parameter(mean=mean, variance=variance, kurtosis=kurtosis, skewness=skewness)
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. |
The parameters are generated on three conditions: 1. $3*kurtosis > 5*skewness^2$, 2. $skewness > 0$, and 3. $variance > 0$.
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. |
Kimihiro Noguchi, Yulia R. Gel
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.
rnig
(in fBasics package)
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"