Generalized Hyperbolic Mode

Computes the mode of the generalized hyperbolic function.

Usage

ghMode(alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)

Arguments

alpha

first shape parameter.

beta

second shape parameter, should in the range (0, alpha).

delta

scale parameter, must be zero or positive.

mu

location parameter, by default 0.

lambda

defines the sublclass, by default \(-1/2\).

Details

The meanings of the parameters correspond to the first parameterization, see gh for further details.

Value

a numeric value, the mode of the generalized hyperbolic distribution

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.

Examples

## ghMode -
   ghMode()
#> [1] -1.344762e-08