Parameter Sets for the Generalized Hyperbolic Distribution
These objects store different parameter sets of the generalized hyperbolic distribution as matrices for testing or demonstration purposes.
The parameter sets ghypSmallShape and
ghypLargeShape have a constant location parameter of
mu = 0, and constant scale parameter delta =
1. In ghypSmallParam and ghypLargeParam 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 ghypChangePars
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.
The values of lambda are drawn from {-0.5, 0, 1} in
ghypSmallShape and {-1, -0.5, 0, 0.5, 1, 2} in
ghypLargeShape.
ghypSmallShape ghypLargeShape ghypSmallParam ghypLargeParam
ghypSmallShape: a 22 by 5 matrix;
ghypLargeShape: a 90 by 5 matrix;
ghypSmallParam: a 84 by 5 matrix;
ghypLargeParam: a 1440 by 5 matrix.
David Scott d.scott@auckland.ac.nz
data(ghypParam)
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 ghypMean
for (i in 1:nrow(ghypSmallParam)) {
param <- ghypSmallParam[i, ]
x <- rghyp(1000, param = param)
sampleMean <- mean(x)
funMean <- ghypMean(param = param)
difference <- abs(sampleMean - funMean)
print(difference)
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