Hyperbolic mode

Computes the mode of the hyperbolic distribution.

Usage

hypMode(alpha = 1, beta = 0, delta = 1, mu = 0, pm = 1)

Arguments

alpha

shape parameter, a positive number. alpha can also be a vector of length four, containing alpha, beta, delta and mu (in that order).

beta

skewness parameter, abs(beta) is in the range (0, alpha).

delta

scale parameter, must be zero or positive.

mu

location parameter, by default 0.

pm

an integer value between 1 and 4 for the selection of the parameterization. The default takes the first parameterization.

Value

a numeric value, the mode in the appropriate parameterization for the 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.

Author

David Scott for code implemented from R's contributed package HyperbolicDist.

Examples

## hypMode -
   hypMode()
#> [1] 0