calculate.range {HyperbolicDist} | R Documentation |
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
.
calculate.range(theta, tol = 10^(-5))
theta |
Value of parameter vector specifying the hyperbolic distribution. |
tol |
Tolerance |
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.
A two-component vector giving the lower and upper ends of the range.
David Scott d.scott@auckland.ac.nz, Jennifer Tso, Richard Trendall
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.
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])