hypMode {fBasics}R Documentation

Hyperbolic Mode

Description

Computes the mode of the hyperbolic function.

Usage

hypMode(alpha = 1, beta = 0, delta = 1, mu = 0, pm = c(1, 2, 3, 4))

Arguments

alpha, beta, delta, mu

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.

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.

Examples

   
## hypMode -
   hypMode()
[Package fBasics version 2160.81 Index]