GeneralizedHyperbolic (version 0.8-6)

hyperbParam: Parameter Sets for the Hyperbolic Distribution

Description

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

The parameter sets hyperbSmallShape and hyperbLargeShape have a constant location parameter of \(\mu\) = 0, and constant scale parameter \(\delta\) = 1. In hyperbSmallParam and hyperbLargeParam 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 hyperbChangePars 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

hyperbSmallShape
  hyperbLargeShape
  hyperbSmallParam
  hyperbLargeParam

Format

hyperbSmallShape: a 7 by 4 matrix; hyperbLargeShape: a 15 by 4 matrix; hyperbSmallParam: a 28 by 4 matrix; hyperbLargeParam: a 240 by 4 matrix.

Author

David Scott

Examples

data(hyperbParam)
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 hyperbMean
for (i in 1:nrow(hyperbSmallParam)) {
  param <- hyperbSmallParam[i, ]
  x <- rhyperb(1000, param = param)
  sampleMean <- mean(x)
  funMean <- hyperbMean(param = param)
  difference <- abs(sampleMean - funMean)
  print(difference)
}