Description Usage Arguments Value Author(s) References See Also Examples
Functions to calculate the mean, variance, skewness, kurtosis and mode of a specific generalized hyperbolic distribution.
1 2 3 4 5 6 7 8 9 10 | ghypMean(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
param = c(mu, delta, alpha, beta, lambda))
ghypVar(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
param = c(mu, delta, alpha, beta, lambda))
ghypSkew(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
param = c(mu, delta, alpha, beta, lambda))
ghypKurt(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
param = c(mu, delta, alpha, beta, lambda))
ghypMode(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
param = c(mu, delta, alpha, beta, lambda))
|
mu |
mu is the location parameter. By default this is set to 0. |
delta |
delta is the scale parameter of the distribution. A default value of 1 has been set. |
alpha |
alpha is the tail parameter, with a default value of 1. |
beta |
beta is the skewness parameter, by default this is 0. |
lambda |
lambda is the shape parameter and dictates the shape that the distribution shall take. Default value is 1. |
param |
Parameter vector of the generalized hyperbolic distribution. |
ghypMean
gives the mean of the generalized hyperbolic distribution,
ghypVar
the variance, ghypSkew
the skewness,
ghypKurt
the kurtosis, and ghypMode
the mode. The
formulae used for the mean is given in Prause (1999). The variance,
skewness and kurtosis are obtained using the recursive formula
implemented in ghypMom
which can calculate moments of
all orders about any point.
The mode is found by a numerical optimisation using
optim
. For the special case of the hyperbolic
distribution a formula for the mode is available, see
hyperbMode
.
The parameterization of the generalized hyperbolic distribution used
for these functions is the (alpha, beta) one. See
ghypChangePars
to transfer between parameterizations.
David Scott d.scott@auckland.ac.nz, Thomas Tran
Prause, K. (1999) The generalized hyperbolic models: Estimation, financial derivatives and risk measurement. PhD Thesis, Mathematics Faculty, University of Freiburg.
dghyp
, ghypChangePars
,
besselK
, RLambda
.
1 2 3 4 5 6 7 8 9 10 11 | param <- c(2, 2, 2, 1, 2)
ghypMean(param = param)
ghypVar(param = param)
ghypSkew(param = param)
ghypKurt(param = param)
ghypMode(param = param)
maxDens <- dghyp(ghypMode(param = param), param = param)
ghypRange <- ghypCalcRange(param = param, tol = 10^(-3) * maxDens)
curve(dghyp(x, param = param), ghypRange[1], ghypRange[2])
abline(v = ghypMode(param = param), col = "blue")
abline(v = ghypMean(param = param), col = "red")
|
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