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\name{nig}
\alias{nig}
\alias{dnig}
\alias{pnig}
\alias{qnig}
\alias{rnig}
\concept{normal inverse Gaussian distribution}
\title{Normal Inverse Gaussian Distribution}
\description{
Density, distribution function, quantile function and random
generation for the normal inverse Gaussian distribution.
}
\usage{
dnig(x, alpha = 1, beta = 0, delta = 1, mu = 0, log = FALSE)
pnig(q, alpha = 1, beta = 0, delta = 1, mu = 0)
qnig(p, alpha = 1, beta = 0, delta = 1, mu = 0)
rnig(n, alpha = 1, beta = 0, delta = 1, mu = 0)
}
\arguments{
\item{x,q}{
a numeric vector of quantiles.
}
\item{p}{
a numeric vector of probabilities.
}
\item{n}{
number of observations.
}
\item{alpha}{
shape parameter.
}
\item{beta}{
skewness parameter \code{beta}, \code{abs(beta)} is in the range
\code{(0, alpha)}.
}
\item{delta}{
scale parameter, must be zero or positive.
}
\item{mu}{
location parameter, by default 0.
}
\item{log}{
a logical flag by default \code{FALSE}. Should labels and a main
title be drawn to the plot?
}
}
\details{
\code{dnig} gives the density.
\code{pnig} gives the distribution function.
\code{qnig} gives the quantile function, and
\code{rnig} generates random deviates.
The parameters \code{alpha, beta, delta, mu} are in the first
parameterization of the distribution.
The random deviates are calculated with the method described by
Raible (2000).
}
\value{
numeric vector
}
\author{
David Scott for code implemented from \R's contributed package
\code{HyperbolicDist}.
}
\references{
Atkinson, A.C. (1982);
\emph{The simulation of generalized inverse Gaussian and hyperbolic
random variables},
SIAM J. Sci. Stat. Comput. 3, 502--515.
Barndorff-Nielsen O. (1977);
\emph{Exponentially decreasing distributions for the logarithm of
particle size},
Proc. Roy. Soc. Lond., A353, 401--419.
Barndorff-Nielsen O., Blaesild, P. (1983);
\emph{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);
\emph{Levy Processes in Finance: Theory, Numerics and Empirical Facts},
PhD Thesis, University of Freiburg, Germany, 161 pages.
}
\examples{
## nig -
set.seed(1953)
r = rnig(5000, alpha = 1, beta = 0.3, delta = 1)
plot(r, type = "l", col = "steelblue",
main = "nig: alpha=1 beta=0.3 delta=1")
## nig -
# Plot empirical density and compare with true density:
hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue")
x = seq(-5, 5, 0.25)
lines(x, dnig(x, alpha = 1, beta = 0.3, delta = 1))
## nig -
# Plot df and compare with true df:
plot(sort(r), (1:5000/5000), main = "Probability", col = "steelblue")
lines(x, pnig(x, alpha = 1, beta = 0.3, delta = 1))
## nig -
# Compute Quantiles:
qnig(pnig(seq(-5, 5, 1), alpha = 1, beta = 0.3, delta = 1),
alpha = 1, beta = 0.3, delta = 1)
}
\keyword{distribution}
|
