ghypB {QRMlib}R Documentation

Univariate Generalized Hyperbolic Distribution B

Description

Density and random number generation for univariate generalized hyperbolic distribution in standard parameterization (alpha-beta-delta). (The dispersion matrix Sigma is identically 1, i.e. a scalar 1.) See pp. 77-81 in QRM.

Usage

dghypB(x, lambda, delta, alpha, beta=0, mu=0, logvalue=FALSE) 
rghypB(n, lambda, delta, alpha, beta=0, mu=0)

Arguments

x values at which to evaluate density
n sample size
lambda scalar parameter
delta scalar parameter
alpha scalar parameter
beta skewness parameter
mu location parameter
logvalue Should log density be returned? Default is FALSE

Details

See page 78 in QRM for joint density formula (3.30) with Sigma (dispersion matrix) the identity and d=1 (meaning a univariate distribution) applies.

The B parameterization corresponds to the original alpha-beta-delta model used by Blaesild (1981) in earlier literature. If gamma is 0, we have a normal variance mixture defined by the paramters alpha-beta-delta. This thickens the tail.

If gamma exceeds zero, we have a normal mean-variance mixture where the mean is also perturbed to equal mu + (W * gamma) which introduces ASYMMETRY as well.

Values for lambda and mu are identical in both QRM and B parameterizations.

Sigma does not appear in parameter list since in the univariate case its value is assumed to be identically 1.

Value

values of density or log-density (dghypB) or random sample (rghypB)

Note

Density values from dgyhp() should be identical to those from dghypB() if the alpha-beta-delta parameters of the B type are translated to the corresponding gamma-chi-psi parameters of the QRM type by formulas on pp 79-80.

Author(s)

documentation by Scott Ulman for R-language distribution

See Also

dghyp, besselM3


[Package QRMlib version 1.4.4 Index]