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\name{adjboxStats}
\alias{adjboxStats}
\title{Statistics for Skewness-adjusted Boxplots}
\description{
Computes the \dQuote{statistics} for producing boxplots adjusted for
skewed distributions as proposed in Hubert and Vandervieren (2008),
see \code{\link{adjbox}}.
}
\usage{
adjboxStats(x, coef = 1.5, a = -4, b = 3, do.conf = TRUE, do.out = TRUE,
\dots)
}
\arguments{
\item{x}{a numeric vector for which adjusted boxplot statistics are computed.}
\item{coef}{number determining how far \sQuote{whiskers} extend out
from the box, see \code{\link{boxplot.stats}}.}
\item{a, b}{scaling factors multiplied by the medcouple
\code{\link{mc}()} to determine outlyer boundaries; see the references.}
\item{do.conf,do.out}{logicals; if \code{FALSE}, the \code{conf} or
\code{out} component respectively will be empty in the result.}
\item{\dots}{further optional arguments to be passed to
\code{\link{mc}()}, such as \code{doReflect}.}
}
\details{
Given the quartiles \eqn{Q_1}{Q1}, \eqn{Q_3}{Q3}, the interquartile
range \eqn{\Delta Q := Q_3 - Q_1}{IQR := Q3-Q1}, and the medcouple
\eqn{M :=}\code{mc(x)}, \eqn{c =}\code{coef},
the \dQuote{fence} is defined,
for \eqn{M \ge 0} as
\deqn{[Q_1 - c e^{a \cdot M}\Delta Q, Q_3 + c e^{b \cdot M}\Delta Q],%
}{[Q1 - c*exp(a * M)*IQR, Q3 + c*exp(b * M)*IQR],}
and for \eqn{M < 0} as
\deqn{[Q_1 - c e^{-b \cdot M}\Delta Q, Q_3 + c e^{-a \cdot M}\Delta Q],%
}{[Q1 - c*exp(-b * M)*IQR, Q3 + c*exp(-a * M)*IQR],}
and all observations \code{x} outside the fence, the \dQuote{potential
outliers}, are returned in \code{out}.
Note that a typo in robustbase version up to 0.7-8,
for the (rare left-skewed) case where \link{mc}(x) < 0, lead to a
\dQuote{fence} not wide enough in the upper part, and hence
\emph{less} outliers there.
}
\value{
A \code{\link{list}} with the components
\item{stats}{a vector of length 5, containing the extreme of the lower
whisker, the lower hinge, the median, the upper hinge and the extreme of
the upper whisker.}
\item{n}{the number of observations}
\item{conf}{the lower and upper extremes of the \sQuote{notch}
(\code{if(do.conf)}). See \code{\link{boxplot.stats}}.}
\item{fence}{length 2 vector of interval boundaries which
define the non-outliers, and hence the whiskers of the plot.}
\item{out}{the values of any data points which lie beyond the fence,
and hence beyond the extremes of the whiskers.}
}
\author{R Core Development Team (\code{\link{boxplot.stats}}); adapted
by Tobias Verbeke and Martin Maechler.}
\note{The code only slightly modifies the code of \R's
\code{\link{boxplot.stats}}.
}
\seealso{\code{\link{adjbox}()}, also for references,
the function which mainly uses this one;
further \code{\link{boxplot.stats}}.
}
\examples{
data(condroz)
adjboxStats(ccA <- condroz[,"Ca"])
adjboxStats(ccA, doReflect = TRUE)# small difference in fence
## Test reflection invariance [was not ok, up to and including robustbase_0.7-8]
a1 <- adjboxStats( ccA, doReflect = TRUE)
a2 <- adjboxStats(-ccA, doReflect = TRUE)
nm1 <- c("stats", "conf", "fence")
stopifnot(all.equal( a1[nm1],
lapply(a2[nm1], function(u) rev(-u))),
all.equal(a1[["out"]], -a2[["out"]]))
}
\keyword{robust}
\keyword{univar}
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