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\name{hypMode}
\alias{hypMode}
\title{Hyperbolic Mode}
\description{
Computes the mode of the hyperbolic function.
}
\usage{
hypMode(alpha = 1, beta = 0, delta = 1, mu = 0, pm = c(1, 2, 3, 4))
}
\arguments{
\item{alpha, beta, delta, mu}{
shape parameter \code{alpha};
skewness parameter \code{beta}, \code{abs(beta)} is in the
range (0, alpha);
scale parameter \code{delta}, \code{delta} must be zero or
positive;
location parameter \code{mu}, by default 0.
These is the meaning of the parameters in the first
parameterization \code{pm=1} which is the default
parameterization selection.
In the second parameterization, \code{pm=2} \code{alpha}
and \code{beta} take the meaning of the shape parameters
(usually named) \code{zeta} and \code{rho}.
In the third parameterization, \code{pm=3} \code{alpha}
and \code{beta} take the meaning of the shape parameters
(usually named) \code{xi} and \code{chi}.
In the fourth parameterization, \code{pm=4} \code{alpha}
and \code{beta} take the meaning of the shape parameters
(usually named) \code{a.bar} and \code{b.bar}.
}
\item{pm}{
an integer value between \code{1} and \code{4} for the
selection of the parameterization. The default takes the
first parameterization.
}
}
\value{
returns the mode in the appropriate parameterization for the
hyperbolic distribution. A numeric value.
}
\references{
Atkinson, A.C. (1982);
\emph{The simulation of generalized inverse Gaussian and hyperbolic
random variables},
SIAM J. Sci. Stat. Comput. 3, 502--515.
Barndorff-Nielsen O. (1977);
\emph{Exponentially decreasing distributions for the logarithm of
particle size},
Proc. Roy. Soc. Lond., A353, 401--419.
Barndorff-Nielsen O., Blaesild, P. (1983);
\emph{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.
Raible S. (2000);
\emph{Levy Processes in Finance: Theory, Numerics and Empirical Facts},
PhD Thesis, University of Freiburg, Germany, 161 pages.
}
\author{
David Scott for code implemented from \R's
contributed package \code{HyperbolicDist}.
}
\examples{
## hypMode -
hypMode()
}
\keyword{distribution}
|
