Parameter Sets for the Normal Inverse Gaussian Distribution

Description

These objects store different parameter sets of the normal inverse Gaussian distribution as matrices for testing or demonstration purposes.

The parameter sets nigSmallShape and nigLargeShape have a constant location parameter of mu = 0, and constant scale parameter delta = 1. In nigSmallParam and nigLargeParam the values of the location and scale parameters vary. In these parameter sets the location parameter mu = 0 takes values from {0, 1} and {-1, 0, 1, 2} respectively. For the scale parameter delta, values are drawn from {1, 5} and {1, 2, 5, 10} respectively.

For the shape parameters alpha and beta the approach is more complex. The values for these shape parameters were chosen by choosing values of xi and chi which range over the shape triangle, then the function nigChangePars was applied to convert them to the alpha, beta parameterization. See the examples for the values of xi and chi for the large parameter sets.

Usage

  nigSmallShape
  nigLargeShape
  nigSmallParam
  nigLargeParam

Format

nigSmallShape: a 7 by 4 matrix; nigLargeShape: a 15 by 4 matrix; nigSmallParam: a 28 by 4 matrix; nigLargeParam: a 240 by 4 matrix.

Author(s)

David Scott d.scott@auckland.ac.nz

Examples

data(nigParam)
plotShapeTriangle()
xis <- rep(c(0.1,0.3,0.5,0.7,0.9), 1:5)
chis <- c(0,-0.25,0.25,-0.45,0,0.45,-0.65,-0.3,0.3,0.65,
          -0.85,-0.4,0,0.4,0.85)
points(chis, xis, pch = 20, col = "red")


## Testing the accuracy of nigMean
for (i in 1:nrow(nigSmallParam)) {
  param <- nigSmallParam[i, ]
  x <- rnig(1000, param = param)
  sampleMean <- mean(x)
  funMean <- nigMean(param = param)
  difference <- abs(sampleMean - funMean)
  print(difference)
}

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GeneralizedHyperbolic)
Loading required package: DistributionUtils
Loading required package: RUnit
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GeneralizedHyperbolic/nigParam.Rd_%03d_medium.png", width=480, height=480)
> ### Name: nigParam
> ### Title: Parameter Sets for the Normal Inverse Gaussian Distribution
> ### Aliases: nigParam nigSmallShape nigLargeShape nigSmallParam
> ###   nigLargeParam
> 
> ### ** Examples
> 
> data(nigParam)
> plotShapeTriangle()
> xis <- rep(c(0.1,0.3,0.5,0.7,0.9), 1:5)
> chis <- c(0,-0.25,0.25,-0.45,0,0.45,-0.65,-0.3,0.3,0.65,
+           -0.85,-0.4,0,0.4,0.85)
> points(chis, xis, pch = 20, col = "red")
> 
> 
> ## Testing the accuracy of nigMean
> for (i in 1:nrow(nigSmallParam)) {
+   param <- nigSmallParam[i, ]
+   x <- rnig(1000, param = param)
+   sampleMean <- mean(x)
+   funMean <- nigMean(param = param)
+   difference <- abs(sampleMean - funMean)
+   print(difference)
+ }
[1] 0.0005446838
[1] 0.03053946
[1] 0.04320501
[1] 0.04120016
[1] 0.0003034942
[1] 0.05964697
[1] 0.1007683
[1] 0.008259733
[1] 0.08602838
[1] 0.1515251
[1] 0.07714651
[1] 0.02651626
[1] 0.03656451
[1] 0.4301991
[1] 0.006592722
[1] 0.0127067
[1] 0.005039324
[1] 0.1495574
[1] 0.06810481
[1] 0.05653211
[1] 0.1073736
[1] 0.02507756
[1] 0.1321643
[1] 0.006780526
[1] 0.7779784
[1] 0.05658183
[1] 0.2546927
[1] 0.4726796
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>