Generalized Hyperbolic Student-t Mode

Computes the mode of the generalized hyperbolic Student-t distribution.

Usage

ghtMode(beta = 0.1, delta = 1, mu = 0, nu = 10)

Arguments

beta

the skewness parameter in the range (0, alpha).

delta

the scale parameter, must be zero or positive.

mu

the location parameter, by default 0.

nu

a numeric value, the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.

Details

These are the parameters in the first parameterization.

Value

a numeric value, the mode for the generalized hyperbolic Student-t 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

## ghtMode -
   ghtMode()
#> [1] 0.009090738