Last data update: 2014.03.03

R: Parameter Sets for the Hyperbolic Distribution
 hyperbParam R Documentation

## 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. 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(s)

David Scott d.scott@auckland.ac.nz

### 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)
}

```

### 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.
'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)
> 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
>

```