swh:1:snp:d1587d616651317fdcebcbb237dce82c32266449
Tip revision: dfe6577bb164f53feaedf2da9530457197edfb1a authored by Georgi N. Boshnakov on 20 October 2022, 11:25:10 UTC
version 4021.93
version 4021.93
Tip revision: dfe6577
dist-ghMoments.Rd
\name{ghMoments}
\alias{ghMoments}
\alias{ghMean}
\alias{ghVar}
\alias{ghSkew}
\alias{ghKurt}
\alias{ghMoments}
\title{Generalized Hyperbolic Distribution Moments}
\description{
Calculates moments of the generalized hyperbolic
distribution function
}
\usage{
ghMean(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghVar(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghSkew(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghKurt(alpha=1, beta=0, delta=1, mu=0, lambda=-1/2)
ghMoments(order, type = c("raw", "central", "mu"),
alpha = 1, beta=0, delta=1, mu=0, lambda=-1/2)
}
\arguments{
\item{alpha, beta, delta, mu, lambda}{
numeric values.
\code{alpha} is the first shape parameter;
\code{beta} is the second shape parameter in the range \code{(0, alpha)};
\code{delta} is the scale parameter, must be zero or positive;
\code{mu} is the location parameter, by default 0; and
\code{lambda} defines the sublclass, by default -1/2.
}
\item{order}{
an integer value, the order of the moment.
}
\item{type}{
a character value,
\code{"raw"} returns the moments about zero,
\code{"central"} returns the central moments about the mean, and
\code{"mu"} returns the moments about the location parameter \code{mu}.
}
}
\value{
a numerical value.
}
\references{
Scott, D. J., Wuertz, D. and Tran, T. T. (2008)
\emph{Moments of the Generalized Hyperbolic Distribution}.
Preprint.
}
\author{
Diethelm Wuertz.
}
\examples{
## ghMean -
ghMean(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
## ghKurt -
ghKurt(alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
## ghMoments -
ghMoments(4,
alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
ghMoments(4, "central",
alpha=1.1, beta=0.1, delta=0.8, mu=-0.3, lambda=1)
}
\keyword{distribution}