Computes the mode of the hyperbolic function.
hypMode(alpha = 1, beta = 0, delta = 1, mu = 0, pm = c(1, 2, 3, 4))returns the mode in the appropriate parameterization for the hyperbolic distribution. A numeric value.
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=2 alpha
and beta take the meaning of the shape parameters
(usually named) zeta and rho.
In the third parameterization, pm=3 alpha
and beta take the meaning of the shape parameters
(usually named) xi and chi.
In the fourth parameterization, pm=4 alpha
and beta take the meaning of the shape parameters
(usually named) a.bar and b.bar.
an integer value between 1 and 4 for the
selection of the parameterization. The default takes the
first parameterization.
David Scott for code implemented from R's
contributed package HyperbolicDist.
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.