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. See the examples for the values of xi and
chi for the large parameter sets.
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)
}
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(GeneralizedHyperbolic)
Loading required package: DistributionUtils
Loading required package: RUnit
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GeneralizedHyperbolic/hyperbParam.Rd_%03d_medium.png", width=480, height=480)
> ### Name: hyperbParam
> ### Title: Parameter Sets for the Hyperbolic Distribution
> ### Aliases: hyperbParam hyperbSmallShape hyperbLargeShape hyperbSmallParam
> ### hyperbLargeParam
>
> ### ** 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)
+ }
[1] 0.001283463
[1] 0.02435437
[1] 0.03841906
[1] 0.1423733
[1] 0.04421782
[1] 0.09400643
[1] 0.2762678
[1] 0.0186508
[1] 0.0809459
[1] 0.08006488
[1] 1.520711
[1] 0.3815463
[1] 0.383951
[1] 0.08939263
[1] 0.005025002
[1] 0.01975047
[1] 0.01102964
[1] 0.06460246
[1] 0.02680613
[1] 0.01428168
[1] 0.02592917
[1] 0.006257403
[1] 0.03218231
[1] 0.01382794
[1] 0.5440419
[1] 0.5723738
[1] 0.4381677
[1] 0.6858696
>
>
>
>
>
>
> dev.off()
null device
1
>