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\name{mle.vonmises.bootstrap.ci}
\title{Bootstrap Confidence Intervals}
\alias{mle.vonmises.bootstrap.ci}
\alias{print.mle.vonmises.bootstrap.ci}
\description{
Generates simple bootstrap confidence intervals for the parameters of a von Mises distribution: the mean direction mu, and the concentration parameter kappa.
}
\usage{
mle.vonmises.bootstrap.ci(x, mu = NULL, bias = FALSE, alpha = 0.05,
reps = 1000, control.circular = list())
\method{print}{mle.vonmises.bootstrap.ci}(x, \dots)
}
\arguments{
\item{x}{vector of angular measurements as a \code{circular} object.}
\item{mu}{If \code{NULL} the value is estimated. This value is used in the bootstrap replications for \code{kappa}.}
\item{bias}{logical, if \code{TRUE}, the replication estimates for kappa are computed with a bias corrected method. See \code{\link{mle.vonmises}}. Default is \code{FALSE}, i.e. no bias correction.}
\item{alpha}{parameter determining level of confidence intervals. 1-alpha confidence intervals for \code{mu} and \code{kappa} are computed. By default, 95\% confidence intervals are generated.}
\item{reps}{number of resampled data sets to use. Default is 1000.}
\item{control.circular}{the attribute of the resulting objects (\code{mu}, \code{mu.ci}).}
\item{\dots}{arguments passed to \code{\link{print.default}}.}
}
\value{
A list is returned with the following components:
\item{mu.ci}{limits of the confidence interval for mu as a \code{circular} object.}
\item{kappa.ci}{limits of the confidence interval for kappa.}
\item{mu}{estimate of mu as a \code{circular} object.}
\item{kappa}{estimate of kappa.}
}
\details{
Percentile confidence intervals are computed by resampling from the original data set \code{reps} times. For each resampled data set, the MLE's of mu and kappa are computed. The bootstrap confidence intervals are the alpha/2 and 1-alpha/2 percentiles of the \code{reps} MLE's computed for each resampled data set.
}
\author{Claudio Agostinelli and Ulric Lund}
\seealso{
\code{\link{mle.vonmises}}
}
\examples{
x <- rvonmises(n=25, mu=circular(0), kappa=3)
x.bs <- mle.vonmises.bootstrap.ci(x, alpha=.10)
par(mfcol=c(1,2))
rose.diag(x.bs$mu, bins=30, main=expression(mu))
hist(x.bs$kappa, main=expression(kappa))
}
\keyword{htest}
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