\name{box}
\alias{box}

\title{Box-Cox Transformation} 

\description{
This function performs Box-Cox transformation on the inputted data matrix.
}

\usage{
box(data, lambda)
}

\arguments{
\item{data}{A numeric vector, matrix or data frame of observations.  Negative data values are permitted.}
\item{lambda}{The transformation to be applied to the data.  If negative data values are present, \code{lambda} has to be positive.}
}

\details{
To allow for negative data values, a slightly modified version of the original Box-Cox (1964) is used here.  This modified version originated from Bickel and Doksum (1981), taking the following form:
\deqn{f(y) = \frac{\mathrm{sgn}(y)|y|^\lambda-1}{\lambda}}{f(y) = ( sgn(y) abs(y)^(lambda) -1 ) / lambda}
When negative data values are involved, the transformation parameter, \eqn{\lambda}{\code{lambda}}, has to be positive in order to avoid discontinuity across zero.
}

\value{
A numeric vector, matrix or data frame of the same dimension as \code{data} is returned.
}

\references{
Bickel, P. J. and Doksum, K. A. (1981) An Analysis of Transformations Revisited. \emph{J. Amer. Statist. Assoc.} \bold{76}(374), 296-311.

Box, G. E. P. and Cox, D. R. (1964) An Analysis of Transformations. \emph{J. R. Statist. Soc. B} \bold{26}, 211-252.
}

\seealso{
\code{\link{rbox}}
}

\examples{
data(rituximab)
data <- exprs(rituximab)
summary(data)
# Transform data using Box-Cox with lambda=0.3
dataTrans <- box(data, 0.3)
# Reverse transform data; this should return back to the original rituximab data
summary(rbox(dataTrans, 0.3))
}

\keyword{math}