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.

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.

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.

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> library(GeneralizedHyperbolic)
Loading required package: DistributionUtils
Loading required package: RUnit
> 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
>