# ghypCalcRange: Range of a Generalized Hyperbolic Distribution In HyperbolicDist: The Hyperbolic Distribution

 ghypCalcRange R Documentation

## Range of a Generalized Hyperbolic Distribution

### Description

Given the parameter vector Theta of a generalized hyperbolic distribution, this function determines the range outside of which the density function is negligible, to a specified tolerance. The parameterization used is the (alpha,beta) one (see `dghyp`). To use another parameterization, use `ghypChangePars`.

### Usage

```ghypCalcRange(Theta, tol = 10^(-5), density = TRUE, ...)
```

### Arguments

 `Theta` Value of parameter vector specifying the hyperbolic distribution. `tol` Tolerance. `density` Logical. If `TRUE`, the bounds are for the density function. If `FALSE`, they should be for the probability distribution, but this has not yet been implemented. `...` Extra arguments for calls to `uniroot`.

### Details

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

If `density = TRUE`, the function gives a range, outside of which the density is less than the given tolerance. Useful for plotting the density. Also used in determining break points for the separate sections over which numerical integration is used to determine the distribution function. The points are found by using `uniroot` on the density function.

If `density = FALSE`, the function returns the message: "`Distribution function bounds not yet implemented`".

### Value

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

### Author(s)

David Scott d.scott@auckland.ac.nz

### References

Barndorff-Nielsen, O. and Bl<e6>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.

`dghyp`, `ghypChangePars`

### Examples

```Theta <- c(1,5,3,1,0)
maxDens <- dghyp(ghypMode(Theta), Theta)
ghypRange <- ghypCalcRange(Theta, tol = 10^(-3)*maxDens)
ghypRange
curve(dghyp(x, Theta), ghypRange[1], ghypRange[2])
## Not run: ghypCalcRange(Theta, tol = 10^(-3), density = FALSE)
```

HyperbolicDist documentation built on March 18, 2022, 6:23 p.m.