R: Range of a Skew Hyperbolic Student t-Distribution
skewhypCalcRange
R Documentation
Range of a Skew Hyperbolic Student t-Distribution
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 or distribution function
are negligible, to a specified tolerance.
Usage
skewhypCalcRange(mu = 0, delta = 1, beta = 1, nu = 1,
param = c(mu,delta,beta,nu), density = TRUE,
tol= 10^(-5), ...)
skewhypStepSize(dist, delta, beta, nu, side = c("right","left"))
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).
density
Logical. If TRUE bounds refer to the density
function, otherwise bounds refer to the distribution function.
tol
Density function value at the endpoints of the range
returned by the function.
dist
Numeric. Current distance value.
side
Character. "right" for a step to the right,
"left" for a step to the right.
...
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 overwriete the other ones. In addition the parameter values are
examined by calling the function skewhypCheckPars to see if
they are valid.
The function skewhypCalcRange returns the range outside of
which the density function or distribution function are less than the
given tolerance. The points are found by using uniroot
on the density or distribution function.
The function skewhypStepSize is used for stepping to the right
or the left to obtain an enclosing interval so uniroot can be
used to search. When the tail is declining exponentially the step is
just a linear function of the current distance from the mode. If the
tail is declining only as a power of x, an exponential step is
used.
skewhypStepSize is for internal use and is not expected to be
called by users. It is documented here for completeness.
Value
The function skewhypCalcRange returns a two component vector
giving the lower and upper limits of the range.