hyperbCalcRange {HyperbolicDist}

Range of a Hyperbolic Distribution

Description

Given the parameter vector Theta 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 (\pi,\zeta) one (see dhyperb). To use another parameterization, use hyperbChangePars.

Usage

hyperbCalcRange(Theta, tol = 10^(-5), density = FALSE)

Arguments

Theta

Value of parameter vector specifying the hyperbolic distribution.

tol

Tolerance.

density

Logical. If FALSE, the bounds are for the probability distribution. If TRUE, they are for the density function.

Details

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

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.

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 [e-mail], Jennifer Tso, Richard Trendall

References

Barndorff-Nielsen, O. and Blæsild, 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.

See Also

dhyperb, hyperbChangePars

Examples

par(mfrow = c(1,2))
Theta <- c(3,5,1,0)
hyperbRange <- hyperbCalcRange(Theta, tol = 10^(-3))
hyperbRange
curve(phyperb(x, Theta), hyperbRange[1], hyperbRange[2])
maxDens <- dhyperb(hyperbMode(Theta), Theta)
hyperbRange <- hyperbCalcRange(Theta, tol = 10^(-3)*maxDens, density = TRUE)
hyperbRange
curve(dhyperb(x, Theta), hyperbRange[1], hyperbRange[2])