Parameter Sets for the Hyperbolic Distribution
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.
hyperbSmallShape hyperbLargeShape hyperbSmallParam hyperbLargeParam
hyperbSmallShape: a 7 by 4 matrix;
hyperbLargeShape: a 15 by 4 matrix;
hyperbSmallParam: a 28 by 4 matrix;
hyperbLargeParam: a 240 by 4 matrix.
David Scott d.scott@auckland.ac.nz
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)
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