ghypB {QRMlib} | R Documentation |
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.
dghypB(x, lambda, delta, alpha, beta=0, mu=0, logvalue=FALSE) rghypB(n, lambda, delta, alpha, beta=0, mu=0)
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 |
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.
values of density or log-density (dghypB) or random sample (rghypB)
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.
documentation by Scott Ulman for R-language distribution