GeneralizedHyperbolic (version 0.8-6)

nigParam: 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. The resulting \(\alpha, \beta\) values were then rounded to three decimal places. 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

David Scott

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)
}