skewhypCalcRange {SkewHyperbolic}R Documentation

Range of a Skew Hyperbolic Student t-Distribuiton

Description

Given the parameter vector param, or parameter values of a skew hyperbolic Student t-distribution, this function determines the range outside of which the density function is negligible, to a specified tolerance.

Usage

skewhypCalcRange(mu = 0, delta = 1, beta = 1, nu = 1,
                 param = c(mu,delta,beta,nu), tol= 10^(-5), ...)

Arguments

mu Location parameter mu, default is 0.
delta Scale parameter delta, default is 1.
beta Skewness parameter beta, default is 1.
nu Shape parameter nu, default is 1.
param Specifying the parameters as a vector of the form
c(mu,delta,beta,nu).
tol Density function value at the endpoints of the range returned by the function.
... Passes additional arguments to uniroot.

Details

The particular skew hyperbolic distribution being considered is specified by either the individual parameter values, or the parameter vector param. If both are specified, the values in param will overwirte the other ones. In addition the parameter values are examined by calling the function skewhypCheckPars to see if they are valid.

The function returns the range outside of which the density is less than the given tolerance. Useful for plotting, and is called by skewhypBreaks when determining suitable breakpoints to be used when integrating the density function numerically to find the distribution function. The points are found by using uniroot on the density function.

Value

The function returns a two component vector giving the lower and upper limits of the range.

Author(s)

David Scott d.scott@auckland.ac.nz, Fiona Grimson

References

Aas, K. and Haff, I. H. (2006). The Generalised Hyperbolic Skew Student's t-distribution, Journal of Financial Econometrics, 4, 275–309.

See Also

uniroot, dskewhyp, skewhypCheckPars

Examples

param <- c(0,1,10,10)
range <- skewhypCalcRange(param = param, tol = 10^(-2))
range
curve(dskewhyp(x, param = c(0,1,5,10), range[1], range[2]))

[Package SkewHyperbolic version 0.1-2 Index]