Last data update: 2014.03.03

R: Range of a Hyperbolic Distribution
 hyperbCalcRange R Documentation

## Range of a Hyperbolic Distribution

### Description

Given the parameter vector param of a hyperbolic distribution, this function calculates the range outside of which the distribution has negligible probability, or the density function is negligible, to a specified tolerance. The parameterization used is the (alpha, beta) one (see `dhyperb`). To use another parameterization, use `hyperbChangePars`.

### Usage

```hyperbCalcRange(mu = 0, delta = 1, alpha = 1, beta = 0,
param = c(mu, delta, alpha, beta),
tol = 10^(-5), density = TRUE, ...)
```

### Arguments

 `mu` mu is the location parameter. By default this is set to 0. `delta` delta is the scale parameter of the distribution. A default value of 1 has been set. `alpha` alpha is the tail parameter, with a default value of 1. `beta` beta is the skewness parameter, by default this is 0. `param` Value of parameter vector specifying the hyperbolic distribution. This takes the form `c(mu, delta, alpha, beta)`. `tol` Tolerance. `density` Logical. If `FALSE`, the bounds are for the probability distribution. If `TRUE`, they are for the density function. `...` Extra arguments for calls to `uniroot`.

### Details

The particular hyperbolic distribution being considered is specified by the value of the parameter value `param`.

If `density = FALSE`, the function calculates the effective range of the distribution, which is used in calculating the distribution function and quantiles, and may be used in determining the range when plotting the distribution. By effective range is meant that the probability of an observation being greater than the upper end is less than the specified tolerance `tol`. Likewise for being smaller than the lower end of the range. Note that this has not been implemented yet.

If `density = TRUE`, the function gives a range, outside of which the density is less than the given tolerance. Useful for plotting the density.

### Value

A two-component vector giving the lower and upper ends of the range.

### Author(s)

David Scott d.scott@auckland.ac.nz, Jennifer Tso, Richard Trendall

### References

Barndorff-Nielsen, O. and Bl<c3><a6>sild, P (1983). Hyperbolic distributions. In Encyclopedia of Statistical Sciences, eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3, pp. 700–707. New York: Wiley.

`dhyperb`, `hyperbChangePars`

### Examples

```par(mfrow = c(1, 2))
param <- c(0, 1, 3, 1)
hyperbRange <- hyperbCalcRange(param = param, tol = 10^(-3))
hyperbRange
curve(phyperb(x, param = param), hyperbRange[1], hyperbRange[2])
maxDens <- dhyperb(hyperbMode(param = param), param = param)
hyperbRange <- hyperbCalcRange(param = param, tol = 10^(-3) * maxDens, density = TRUE)
hyperbRange
curve(dhyperb(x, param = param), hyperbRange[1], hyperbRange[2])
```

### 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/hyperbCalcRange.Rd_%03d_medium.png", width=480, height=480)
> ### Name: hyperbCalcRange
> ### Title: Range of a Hyperbolic Distribution
> ### Aliases: hyperbCalcRange
> ### Keywords: distribution
>
> ### ** Examples
>
> par(mfrow = c(1, 2))
> param <- c(0, 1, 3, 1)
> hyperbRange <- hyperbCalcRange(param = param, tol = 10^(-3))
> hyperbRange
[1] -2.123201  4.414176
> curve(phyperb(x, param = param), hyperbRange[1], hyperbRange[2])
> maxDens <- dhyperb(hyperbMode(param = param), param = param)
> hyperbRange <- hyperbCalcRange(param = param, tol = 10^(-3) * maxDens, density = TRUE)
> hyperbRange
[1] -2.276609  4.710633
> curve(dhyperb(x, param = param), hyperbRange[1], hyperbRange[2])
>
>
>
>
>
> dev.off()
null device
1
>

```