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\name{wrappedNormal}
\title{Wrapped Normal Density Function}
\alias{dwrappednormal}
\alias{rwrappednormal}
\alias{pwrappednormal}
\alias{qwrappednormal}
\description{
Density, and random generation for the wrapped normal circular distribution.
}
\usage{
rwrappednormal(n, mu = circular(0), rho = NULL, sd = 1,
control.circular = list())
dwrappednormal(x, mu = circular(0), rho = NULL, sd = 1,
K = NULL, min.k = 10)
pwrappednormal(q, mu = circular(0), rho = NULL, sd = 1,
from = NULL, K = NULL, min.k = 10, \dots)
qwrappednormal(p, mu = circular(0), rho = NULL, sd = 1,
from = NULL, K = NULL, min.k = 10, tol = .Machine$double.eps^(0.6),
control.circular = list(), \dots)
}
\arguments{
\item{x, q}{vector of quantiles. The object is coerced to class
\code{\link{circular}}.}
\item{p}{vector of probabilities.}
\item{n}{number of observations.}
\item{mu}{mean direction of the distribution as a \code{circular} object.}
\item{rho}{concentration parameter of the distribution. \code{rho}
must be in the interval from 0 to 1.}
\item{sd}{standard deviation of the (unwrapped) normal distribution.}
\item{from}{if \code{NULL} is set to \eqn{mu-pi}. This is the value from which the pwrappednormal and qwrappednormal are evaluated. It should be a \code{circular} object.}
\item{K}{number of terms to be used in approximating the density.}
\item{min.k}{minimum number of terms used in approximating the density.}
\item{tol}{passed to \code{\link{uniroot}}.}
\item{control.circular}{the attribute of the resulting object.}
\item{\dots}{parameters passed to \code{\link{integrate}}.}
}
\value{
\code{dwrappednormal} gives the density and \code{rwrappednormal}
generates random deviates, \code{pwrappednormal} gives the
distribution function, and \code{qwrappednormal} provides quantiles.
}
\author{Claudio Agostinelli and Ulric Lund}
\references{
Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 2.2.7, World Scientific Press, Singapore.
}
\examples{
data1 <- rwrappednormal(100, mu=circular(0), rho=0.7,
control.circular=list(units="degrees"))
plot(data1)
ff <- function(x) dwrappednormal(x, mu=circular(pi), rho=0.7)
curve.circular(ff, join=TRUE, xlim=c(-1.5, 1),
main="Density of a Wrapped Normal Distribution \n mu=pi, rho=0.7")
ff <- function(x) pwrappednormal(x, mu=circular(pi), rho=0.7)
curve.circular(ff, join=FALSE, xlim=c(-2, 2), ylim=c(-2, 2),
to=(2*pi-3*.Machine$double.eps), modulo="asis", nosort=TRUE,
main="Probability of a Wrapped Normal Distribution \n mu=pi,
rho=0.7, from=0")
ff <- function(x) pwrappednormal(x, mu=circular(pi), rho=0.7, from=circular(pi))
curve.circular(ff, join=FALSE, xlim=c(-2, 2), ylim=c(-2, 2), from=-pi,
to=(pi-3*.Machine$double.eps), modulo="asis", nosort=TRUE,
main="Probability of a Wrapped Normal Distribution \n mu=pi,
rho=0.7, from=pi")
plot(qwrappednormal, from=0, to=1)
plot(function(x) qwrappednormal(p=x, mu=circular(pi)), from=0, to=1)
}
\keyword{distribution}
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