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\name{totalvariation.circular}
\alias{totalvariation.circular}
\title{
Conditional total variation distance between two circular samples.
}
\description{
The total variation distance between two circular samples is
evaluated conditional on a circular modal region.
}
\usage{
totalvariation.circular(x, y, z = NULL, q = 0.95, bw, adjust = 1,
type = c("K", "L"), kernel = c("vonmises", "wrappednormal"),
na.rm = FALSE, step = 0.001, eps.lower = 10^(-4), eps.upper = 10^(-4), ...)
}
\arguments{
\item{x}{numeric or an object of class \code{\link{circular}}.}
\item{y}{numeric or an object of class \code{\link{circular}}.}
\item{z}{numeric or object of class \code{\link{circular}}. The grid
were the kernel density estimate will be evaluated. If \code{NULL}
equally spaced points in the interval [0,2*pi) with step \code{step}.}
\item{q}{numeric in the interval [0,1]. The quantile of the modal
region.}
\item{bw}{the smoothing bandwidth to be used. When the \code{kernel}
is \code{vonmises} the bandwidth is equal to the concentration
parameter.}
\item{adjust}{the bandwidth used is actually \code{adjust*bw}. This
makes it easy to specify values like ``half the default bandwidth''.}
\item{type}{Not Yet Used.}
\item{kernel}{a character string giving the smoothing kernel to be
used. This must be one of \code{"vonmises"} or
\code{"wrappednormal"}, that are kernels of \code{type} \code{"K"}.}
\item{na.rm}{logical; if \code{TRUE}, missing values are removed from
\code{x}. If \code{FALSE} any missing values cause an error.}
\item{step}{numeric. Used in the construction of the regular grid \code{z}.}
\item{eps.lower,eps.upper}{the cut point in the density is searched in
the interval [min(density)*(1+eps.lower),max(density)*(1-eps.upper)].}
\item{\dots}{further arguments passed to the
\code{modal.region.circular} function. Not used at present.}
}
\value{
A list of class \code{totalvariation.circular} with the following
components
\item{tv}{the (conditional) total variation.}
\item{ovl}{the (conditional) overlapping coefficient.}
\item{q}{the order of the modal regions.}
\item{bw}{the bandwidth value as in input.}
\item{modal.x}{an object of class \code{\link{modal.region.circular}}
for the \code{x} data set.}
\item{modal.y}{an object of class \code{\link{modal.region.circular}}
for the \code{y} data set.}
\item{density.x}{an object of class \code{\link{density.circular}}
for the \code{x} data set.}
\item{density.y}{an object of class \code{\link{density.circular}}
for the \code{y} data set.}
\item{density}{a function which report the positive part of the
difference between the estimated density of the two data sets.}
}
\references{
L.G.R. Oliveira-Santos, C.A. Zucco and C. Agostinelli (2013) Using
conditional circular kernel density functions to test hypotheses on
animal circadian activity. Animal Behaviour, 85(1) 269-280.
}
\author{
Claudio Agostinelli
}
\seealso{
\code{\link{modal.region.circular}}
}
\examples{
x <- rvonmises(100, circular(pi), 10)
y <- rvonmises(100, circular(pi+pi/8), 10)
res <- totalvariation.circular(x,y,bw=50)
plot(res)
}
\keyword{univariate}
|
