shape parameter alpha;
skewness parameter beta, abs(beta) is in the
range (0, alpha);
scale parameter delta, delta must be zero or
positive;
location parameter mu, by default 0.
These is the meaning of the parameters in the first
parameterization pm=1 which is the default
parameterization selection.
In the second parameterization, pm=2alpha
and beta take the meaning of the shape parameters
(usually named) zeta and rho.
In the third parameterization, pm=3alpha
and beta take the meaning of the shape parameters
(usually named) xi and chi.
In the fourth parameterization, pm=4alpha
and beta take the meaning of the shape parameters
(usually named) a.bar and b.bar.
pm
an integer value between 1 and 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.
Author(s)
David Scott for code implemented from R's
contributed package HyperbolicDist.
References
Atkinson, A.C. (1982);
The simulation of generalized inverse Gaussian and hyperbolic
random variables,
SIAM J. Sci. Stat. Comput. 3, 502–515.
Barndorff-Nielsen O. (1977);
Exponentially decreasing distributions for the logarithm of
particle size,
Proc. Roy. Soc. Lond., A353, 401–419.
Barndorff-Nielsen O., 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.
Raible S. (2000);
Levy Processes in Finance: Theory, Numerics and Empirical Facts,
PhD Thesis, University of Freiburg, Germany, 161 pages.