calculate.range {HyperbolicDist}R Documentation

Range of a Hyperbolic Distribution

Description

Given the parameter vector theta of a hyperbolic distribution, this function calculates the range over which the distribution is non-zero, to a specified tolerance. The parameterisation used is the pi/zeta one (see dhyperb). To use another parameterisation, use hyperb.change.pars.

Usage

calculate.range(theta, tol = 10^(-5))

Arguments

theta Value of parameter vector specifying the hyperbolic distribution.
tol Tolerance

Details

The particular hyperbolic distribution being considered is specified by the value of the parameter value theta. The function calculates the effective range of the distribution, which is useful in calculating the distribution function and quantiles, but also in determining the range when plotting the density. 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.

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 Blaesild, 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, hyperb.change.pars

Examples

hyperb.range <- calculate.range(c(3,5,1,0),tol=10^(-2))
curve(dhyperb(x,c(3,5,1,0)),hyperb.range[1],hyperb.range[2])

[Package HyperbolicDist version 0.0-1 Index]