nigParam {GeneralizedHyperbolic} | R Documentation |
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
= 0, and constant scale parameter
=
1. In
nigSmallParam
and nigLargeParam
the values of
the location and scale parameters vary. In these parameter sets the
location parameter = 0 takes values from {0, 1} and
{-1, 0, 1, 2} respectively. For the scale parameter
, values are drawn from {1, 5} and {1, 2, 5,
10} respectively.
For the shape parameters and
the
approach is more complex. The values for these shape parameters were
chosen by choosing values of
and
which
range over the shape triangle, then the function
nigChangePars
was applied to convert them to the
parameterization. The resulting
values were then rounded to three decimal places. See the examples for
the values of
and
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)
}